As any normal child would, Harry missed his parents and made it known to everyone he came into contact with, which earned much sympathy from most, and a bit of annoyance and much impatience from his aunt and uncle. Truthfully, Jackie was also starting to become annoyed with the poor child by half-way through December. It seemed as if fighting off the curse residue had tired him out the first week to the point where he was very easy to handle and spent much of his time resting. After having been cleansed, however, he returned to his normal energetic self. Though a generally happy child, Harry was very active and had a habit of investigating everything he could get his hands on. He also had a hard time going to sleep, continually asking for his parents until his tiredness forced him to rest.
After the first few weekends, Jackie gave up and snuck in a Good Knight pillow, which was charmed to be comforting and guarded against nightmares while being safe for young children. This meant he could be put to sleep in half an hour instead of the previous two hours. Jackie's agreement with Dursleys prevented magical toys and books, but said nothing about magical pillows. To be frank, since this also reduced the time Petunia spent putting Harry to sleep, she was willing to pretend ignorance. She even started sending Harry to daycare with the pillow once his nannies complained about his difficulties during nap times, though they were very sympathetic to poor orphan Harry.
Another thing that helped was having pictures of his parents near him. Jackie was able to convince Petunia to write to Minerva McGonagall asking for pictures of Lily and James Potter. Jackie made non-magical copies of the dozen photographs that were sent back to put near Harry's bed while the originals went to the corner of Jackie's living room where Harry's things were stored. Most of them were of Lily or James in school uniforms, though there was one from their wedding day and another from when they had announced Lily's pregnancy. The original magical version of the last Petunia was kind enough to allow Jackie to keep in Harry's room. This calmed Harry down as he could wave hello to his parents before going to sleep or leaving the house. Vernon so rarely entered Harry's room that he never noticed its presence.
Harry had so far managed to avoid obvious acts of magic which resulted in the Dursleys being more comfortable around him. Dudley, the over-indulged beach ball that he was, had at first been aggressive to Harry and attempted to steal his toys, but Harry had given as good as he got and Dudley soon learned to leave him alone. The Dursley parents couldn't claim that Harry was the aggressor because Jackie made several surprise appearances the first two months and saw how the two cousins interacted. Dudley's time in daycare further socialized him, forcing his parents to teach him to share and play nice with other children if they didn't want him to be thrown out. Petunia's wage, while not extravagant, was very helpful to the young family and they didn't want to lose it and curtail their spending, which would happen if Dudley didn't have a daycare to go to.
Vernon never did warm up to Harry, and the two tended to avoid each other, usually only spending time together during mealtimes. They could go weeks with barely a word between, except for the odd order of 'Boy, do this' or 'Boy, don't do that'. And while Petunia was closer to Harry, that was mostly because she had to be. Until he learned to bathe, feed and clothe himself, and was potty trained, she took care of those aspects of his care during the weekdays. And when he got older, she supervised his chores, his weekday schedule, and was considered his primary guardian by the wider public. As the Dursleys didn't see much in the way of added costs to housing Harry, and they benefited both from the blood wards and from being able to claim a moral high ground for caring for an orphan child out of the goodness of their heart, they were willing to tolerate him. Jackie's keen oversight helped to prevent them from being too callous towards the boy, but it said something when Harry had to be reminded to refer to Petunia as his aunt rather than as Mrs. Dursley, while he had no problem referring to Jackie as 'auntie'.
Up to the age of five, Harry's weekends with Jackie consisted mostly of him playing with magical toys in the living room with Jackie doing paperwork on the dining room table. She also read him magical children's tales and took him out to nearby children's park to play with neighboring muggle children. She had told everyone that Harry was her godson and she shared custody with his elderly aunt and uncle, which is why she only had him for the weekends. Due to his age, none of the muggles took Harry's mumblings about magic toys and moving pictures seriously and assumed they were robotic toys or video recordings. She didn't take him to museums and zoos because his daycare center had regular 'educational' trips that he took part in. Sometimes they would ask for funds for special lunches or ticket fares, and usually Jackie was able to stretch Harry's trust fund payments to cover them. When she couldn't, well, she was willing to pay the difference for someone who single-handedly stopped a terrorist organization. Any money spent on birthday presents for his friends was made up for by the presents he received for his birthdays, especially from his aunt and uncle who were willing to hand over cash that could be added to Harry's budget; by this point, Vernon had been promoted and Petunia had received regular raises, leading to a very comfortable life for the Dursleys, and they preferred to hand over an envelope of cash rather than go to the bother of actually shopping for him.
A few weeks before Harry's fifth birthday the first treasury bond matured and was cashed in on Harry's behalf by Jackie. Part of the £1160 (the rest was put in a high-interest savings account) was used to buy Harry 'big boy' furniture for his birthday. Jackie had originally bought him a small toddler bed which he had been sleeping on for a while, but he was getting too tall and needed a proper twin sized bed.
Since the toddler furniture Harry had was actually very good quality and had been refurbished (with magic) by Jackie but was not actually magical, she was able to sell it to a secondhand store. The additional money was added to the general budget and she took Harry furniture shopping for the first time in his young life.
Jackie was still unwilling to waste money on brand new furniture when she could buy second hand, but she and Harry made a weekend of it, visiting dozens of secondhand furniture stores before finding a solidly built set that Harry liked. The set was again wooden and consisted of bed frame, side table, a wardrobe (which had a mirror inside its door), a desk and chair, and a narrow bookcase. After magically fixing and cleaning it, the set showed itself to be made from pine wood, which was a nice light grained wood that helped brighten up Harry's room. As he didn't actually sleep at Jackie's (and she didn't have a second bedroom) Harry didn't have a room at her flat, which was great as it meant that he subconsciously considered #4 to be his home. They also purchased a nice rug with an animal design and a reading light for his bed.
His friends had drawn him colorful pictures to give to him for his birthday (along with clothes and a few toys) which he hung on the walls. Though he actually did not like the shopping frenzy, Harry loved his new room. His enthusiasm was reduced when he (and Dudley) were informed that as they were now old enough to go to school, they were old enough to be responsible for keeping their rooms clean and would be grounded if they didn't.
Five was also the age that Jackie began to train Harry to keep the magical world a secret. Growing up, he had been told certain things (like how his toys would magically fix themselves or how his healers had wands that threw bright colors instead of stethoscopes and needles) were to be kept secret and should not be spoken about to his friends. Now that he was leaving daycare behind, comments about moving pictures and talking chess pieces could not be explained away as a toddler not understanding what he was looking at. Therefore, Harry had to be much more guarded about what he said to people other than Jackie, and he was not to mention anything about magic to Dudley.
This was helped by the fact that the primary school Harry and Dudley were going to was far away from their daycare which meant most of Harry's daycare friends did not end up going there. Harry had had only limited contact with the children in Little Whinging due to spending most of his time at daycare or Jackie's. As such, Harry's new friends would not be expecting him to tell them about what new wonders his 'imagination' could come up with, and Dudley had been told by his father that big boys did not believe in magic. As such, both boys were aware not to introduce that topic of conversation, though it still took all summer for the lessons to truly stick.
The second (and final; Lily had only purchased two before her death) treasury bond matured a year later and it was added to the existing saving account which was accessed by Jackie once a year for Harry's birthday. This was in order to purchase magical presents for Harry's birthdays - a Little Potioneer potions kit for his seventh birthday, tickets to a handful of Quidditch games for his eighth, Quidditch tickets (Jackie had created a monster) and a wizarding radio (to keep up with Quidditch results) for his ninth, and season tickets for his tenth (she had given up by that point). Unfortunately, these all had to be kept secret from Dudley, so Harry had to pretend that he had only gotten new clothes (purchased with the monetary gift from Petunia and Vernon) for his birthdays.
Dudley and Harry were not actually close friends; they hadn't been in daycare and a friendship between them didn't develop in the years after, in large part due to the secrecy. They were friendly due to living together, and they did consider each other family, but they had different groups of friends and interests. Dudley was big-boned and aggressive for his age, though his parents had made some effort to curb his tendency towards bullying (mostly because other parents complained about it). Harry was average in size for his age and sweet-natured, though he could get very stubborn and was often described as cheeky by his teachers. Both were involved in Boy Scouts, junior football, and Petunia had insisted on piano lessons for both back when the boys were four years old (Mrs. Polkiss from down the street was a piano teacher) if only to give her an extra six hours of peace every week. This was where Dudley had first met his best friend, Piers Polkiss, who had a similarly aggressive attitude. Unfortunately, they both switched instruments, Dudley for drums and Harry for violin (partly because Jackie wasn't sure if Hogwarts had a piano and a violin would better fit in his trunk). Harry still played the piano occasionally since Jackie inherited one from her parents, but he enjoyed the violin more. They both also had chores - Harry had to take out the garbage and wash dishes (Dudley could not be trusted with breakables) while Dudley had to water the yard and go around the house gathering the dirty laundry. As they got older, vacuuming and washing the car were added to their respective chore lists too.
It should also be said that Harry was significantly brighter than Dudley, though that could be due to Jackie's and Vernon's individual influences. Vernon did not expect his son to be a 'pansy bookworm' and so was happy with average results (and even that was mostly because Petunia wanted her son to get passing grades). Jackie, meanwhile, expected Harry to do his work to the best of his ability and was willing to spend time tutoring him if he needed it. Harry was also more willing to sit still and pay attention to his teachers as good reports from them were rewarded with lessons on magic and incognito visits to magical locations like Hogsmeade. Harry was also aware (because Jackie kept harping on about it) that his time in a muggle school was limited and he needed to take advantage of it while he could.
His 'magic' lessons were less magical and more pragmatic; he learned to neatly write with a quill (a fancy one that had an endless supply of rainbow colored ink), how to properly format essays, and was given access to books on magical history, which were more like fantasy novels than anything else. Harry also enjoyed looking through the Daily Prophet, which usually had very entertaining articles and even more entertaining pictures.
Starting in the summer of his tenth birthday, Harry's lessons with Jackie became more structured. He was given an allowance of £50 a week (no fees for daycare meant Jackie's budget for Harry wasn't as tight) that he had control over, though he had to explain to Jackie every month how he spent the money and Jackie used the opportunity to teach him financial common sense such as saving 20% of his earnings. Most of the money went towards school trips and outings with friends, but the £10 went towards a piggy bank for birthday gifts. He also started learning basic safety rules and beginning theory for potions, charms and transfiguration, and started learning about astronomy and herbology. Along with that, he voluntarily read parts of Hogwarts: A History (mostly about the different houses), and started spending part of each weekend in the magical world to better fit in once he got to Hogwarts. Jackie's first term at Hogwarts had been a huge adjustment with only her status as a muggleborn saving her from teasing from her year mates. As a half-blood, everyone would expect Harry to be familiar with the magical world, and him not being so would make him look like an idiot.
As he got older, Harry couldn't help but notice that there some people he would more likely than not meet every time he stepped into the magical world. It began with meeting Professor McGonagall at one of his first Quidditch games, then Professors Flitwick and Sprout began to make appearances, and more recently Neville Longbottom, a boy his own age, and his grandmother, Madame Longbottom. Harry didn't mind - knowing some of his Hogwarts professors helped him feel less uncomfortable about leaving his family for months at a time, and Neville was a nice boy who could be convinced to play pretend aurors under the Quidditch stands. He was even invited to Neville's last couple of birthdays, which was great as Neville's family lived in an isolated plot of land and had a couple of broomsticks the boys were allowed to use (Jackie had worked very hard to convince Madame Longbottom, but when Neville proved capable of flying a broomstick, Madame had seemed oddly relieved).
What did worry Harry was that even though he introduced himself as Henry Morse, and had had the usual color charms on, he was sure they all knew who he really was. Jackie had told him what had happened to his parents, and how everyone expected him to be some great hero, but that wasn't Harry. He didn't want people to expect so much from him and while he loved his parents (or their memory) he knew he only looked like them; he didn't like pranking like his father did when he was Harry's age and he wasn't the social butterfly his mother was. Perhaps it was due to having to keep so many secrets, but Harry was friendly to most of his classmates, but only friends with a few, and he didn't want to change that. And while Harry loved a good laugh as much as anyone, he wasn't the class clown, nor was he the most clever student in his school.
When he had brought up his worries to Jackie she had only smiled proudly down on him. "You're right, they do know who you are. At first McGonagall was worried to see you with me, but when I explained the trust fund, she was willing to stay out of it, though she did ask to be kept updated on how you were doing. I didn't feel like being her informant - that means spy - so instead I would only tell her what tickets I had bought you. Outside of Quidditch, the child friendly areas of magical Britain are so limited, it is very easy to determine where a young child could be, especially if you know when he will most likely be out the house."
"And Neville? Is he my friend, or…?" Harry was too scared to finish his sentence. Neville was his only magical friend, and they wrote letters to each other all the time as well as saw each other most weekends. He had been so excited to be going to Hogwarts with a friend already made, but now that could all be ruined.
"Harry, is Neville the type of person who would do that?" Jackie asked him gently.
Harry shook his head quickly with a relieved smile.
"Neville was not told, but his grandmother believes he suspects. He's a nice boy, and is polite enough not to confront you on it." Jackie should have seen this conversation coming, but honestly, as the uninteresting daughter of an uninteresting family, she never had been in a situation like this. Hopefully, she had said enough to make Harry feel better; she didn't want to him to ever feel like he wasn't appreciated just for being himself.
"Do you- do you think I should tell him?" Harry asked with a slightly queasy look though there was hope in his eyes.
"I think you should do what makes you feel comfortable." Jackie said firmly. She only had a few months left before Harry started leaving for most of the year and she needed him to be able to make decisions for himself. It was unfair of her perhaps, but as an orphan with a lot of media attention, Harry needed to act with a maturity most children could avoid. She could only protect him for so long, especially as she had no familial link to him. Solicitors were not actually supposed to be as emotionally invested in their clients as she was, which meant her position as his trustee (and for his muggle trust fund only at that) really didn't stand a chance in the face of someone like Dumbledore or even Malfoy. Harry needed to be able to count on himself to make the right decisions without her input, and this was a safe first attempt.
"That's not an answer!" Harry complained, which only caused Jackie to smirk. "I'll think about it." Harry took a deep breath and then looked uncomfortably to the side. "What about the other part? About being Harry Potter and everything?"
Jackie sighed and lead Harry to sit on the living room sofa. "You're right there, too. Some people, a lot of people, already have an idea of who Harry Potter should be, but you shouldn't worry about it. Be yourself. You may not be the smartest, but you are smart. You may not be the funniest, but you have a great sense of humor." Jackie put her hand under Harry's chin and forced him to meet her eye. "I only knew you parents once they were already adults, so I don't really know what they were like when they were children. You would have to ask the professors for more stories for that. But, from when I knew them, they were a lot like you. They both had a good sense of humor, a close but small circle of trusted friends, and both were very smart, not from having a lot of information, but from being curious, just like you. Like you, they investigated anything that caught their attention and liked to know how and why things worked. From what I remember, you are a lot like your parents, albeit when they were older and more mature. Alright?"
Harry's face had cheered up by the end of Jackie's speech, and he smiled and nodded. He was more than alright - Jackie was right. He was like his parents where it counted, and yet different enough to be his own person. Harry Potter may be famous, but Hadrian James Potter was going to knock the Wizarding World's socks off!