So, Cat has two kind of magic. I use two terms for it:
-her "powers", inherited from her universe and which she controls perfectly
-"magic" properly speaking, from HP universe, which she will learn in Hogwarts!
And before you read, when you put "-san" after a name in Japanese, it means Mr or Mrs. Since Cat comes from a world similar to feudal Japan, she uses the terms to speak of her family.
CATTLEYA'S POV
Cat was standing in front of the bar, holding Keikoku's hand in hers. "The Leaky Cauldron" said the sign. So, here we are.
It had been decided that Cat and Keikoku would spend the summer with Professor Dumbledore. After the night they had appeared in the headmaster's office, Cat had told both men about her story.
They had been extremely impressed by Cat's description of her world and family. Indeed, although some people had abilities different to that of a normal human being, it was very different from what was called "magic" in the world she was currently in.
In her world, there were two kinds of populations.
The first one were normal people, they were very close to what Dumbledore had called "Muggles": human beings with no special ability. They were an enormous majority.
Then, there were the Chaman. Every Chaman had a power specific to them: her mother's was to see the future in the sky, her uncle had been able to know someone's past just by touching them, she had heard of Chaman that could make flowers out of rocks… It was not an ability passed down from generation to generation but a trait that randomly emerged in some people; therefore it did not exactly count as magic.
And then there was her clan. The Mibu. An ancient family, that had powers neither normal humans nor Chaman had, but not really a population either. They had kept to themselves and had remained hidden in the heart of a forest, for humans and Chamans feared and hated them. Cat had told them about the disease that had started affecting her whole clan a generation before she was born and was quickly spreading. Her mother, the clan's Seer, had foretold that Cat was the only one who could find a way to cure the disease, and Cat had left the clan, searching for places and families known for their knowledge in medicine. She had known of her ability to travel through space since childhood, and her father had explained her that other universes existed, therefore, after 4 years of fruitless research in her own world, she had decided to try her luck in another universe.
Cat sighed. Truth be told, she had withheld some piece of information. She had not told them about how developed her clan's powers were. Moreover, she had passed quickly on how she had met Keikoku "on the way" and decided to take him along as her little brother. She glanced at the boy and smiled to herself. She had been taking care of him for the last 3 years, he had accompanied her in all her travels and she was very fond of him. Most people were afraid of his red eyes, and of the aura he emitted, but Cat knew better. She knew just how cruel the world could be to those who were different, and she didn't mind the fact that he was not exactly the bubbly-wobbly, happy-go-lucky kind of child that adults loved. He had his own ways to show her he cared, and that was enough to her.
"Kei, we're supposed to go in there and ask for the barman. Ah! Wait, what was his name again?" Cat smacked herself mentally for her lack of memory whenever it came to names. "Mmm, it was a short name… Wait… I know… Awwwww I'm so frustrated" She took her head in her hands and started shaking it frantically
"Tom" her brother replied in a quiet tone. Cat beamed at him "Kei, you're a genius" she knelt and pulled her brother in a hug with a rather goofy smile on her face.
"You're the one who's stupid. And get off me, girl" the boy answered.
"Don't call your beloved older sister girl, you ungrateful little demon!" she exclaimed, only to tighten her hold on him and plant a firm kiss on his cheek, which he took with a rather bored look.
"… Whatever"
"Hey! Don't whatever me!" she was standing again, waving a menacing finger at him.
Keikoku stared back, turned away, and entered the bar
"Hey! Don't ignore me either! Kei! Yo! Keikoku! COME BACK AT THIS INSTANT! GAAAAAAA"she followed him inside.
And with that, they entered Diagon Alley to by the wand she needed.
DUMBLEDORE'S POV
Dumbledore was preparing his lessons for the year that was about to start at Hogwarts. He paused in his work to consider the two kids he was taking care of during the summer. After Miss Mibu had told him about her reasons for travelling to this world, he had had a small discussion with Armando.
FLASHBACK
"- Armando, it is obvious that the girl has not only inherited her family's own power. Magic is running in her veins. You can feel it too, can't you?
- And what exactly are you implying Albus? That we should take her into Hogwarts and teach her our ways? The headmaster clearly viewed this suggestion as ludicrous
-…
-Oh, no no no Albus, I know that look, really! The girl is seventeen, for Merlin's sake, and she doesn't even know the basics of magic.
- Well, I will teach her whatever I can during the summer, and then we can see in September in which year we should put her. She certainly looks clever enough to make it to a 4th year.
- A fourth year? In two months? Please Albus, you obviously overestimate the girl…
- Either that, or you underestimate her Armando.
After a small staring match:
-Fine. You do what you want, as usual. But Albus, the war is going on, how will you teach her?
- I will find a way."
END OF FLASHBACK
And so Dumbledore had taken both children in for the summer, providing the older one with all the books of the 7 years at Hogwarts. He had seen work over them and study about 15 hours a day. She had spent the rest of her time with her brother. The bond between them was clearly strong. Most of the time, they would only lay outside on the grass or sit in the same room, each one reading a book, but Albus knew that real care did pass through actions and not through useless babbling. He chuckled at the memory of his argument with the girl.
FLASHBACK
"-Miss Mibu, could I have a word with you? He had asked her two days after her arrival. Mr Dippet and myself have recognized the unmistakable mark of magic in you. We have decided to offer you a place in Hogwarts, the witch and wizard academy.
- What about Keikoku? She had asked at once
- I will see that he is taken care of.
- Then my answer is no, she had replied flatly.
Dumbledore certainly had not expected that. Quickly regaining his composure, he asked:
-May I know why?
- Sir, please. Because my brother has red eyes, because he is not the talkative child, because he never displays emotions, people call him a little demon and throw stones at him at worst, or try to avoid him at best. I will not have my brother taken care of by someone who thinks he is a freak, she answered calmly. Dumbledore could not help but admire the girl. She had not raised her voice once, her body was very still, yet she had looked quite…powerful at that instant. He could not help but think that she had the fabric to be a leader.
- Miss Mibu, I can assure you that I will find the adequate person for the job. And if you are to find a way to cure your family, what better way is there but to learn magic? He saw her falter at that argument
-…
- Miss Mibu, you need to make a decision right now. Forgive me for my bluntness but you are very, very late by our standards and have a lot to catch up. The girl actually smiled,
- I understand Sir. I appreciate your honesty. Fine then, let me talk to him. And I will catch up all right."
END OF FLASHBACK
And catch up she had. It was obvious that she loved to learn. She had gotten all her potions from 1st to 6th year perfectly on the first attempt. She had mastered charms, transfiguration and DADA until 4th grade impressively quickly too. She was currently working on 5th and 6th grade level spells. Her problem was with transfiguration, and see as he was the transfiguration teacher, he had helped her alright.
FLASHBACK
"- Well, I certainly am most impressed at your catching up Miss Mibu!
She had beamed at that comment:
- Well, I have always loved learning. I would spend hours a day reading my clan's archives on my own, and I quite a lot of teachers willing to help… Yuan-san taught me how to master fire and Shinrei-san how to master water… Father taught me how to master the wind…Akari-san introduced me to the art of healing….
- You must miss them all, Dumbledore interrupted her tactfully, hearing her voice falter.
The girl kept her head bent for a few seconds, but when she held it up, her eyes were dry
- I do miss them, I think about them every day and they keep me strong. All that matters is that I find a cure for the illness so we can all have fun together like with used to."
She had that serene smile on her face and her gaze was full of that patient, everlasting determination he had so rarely seen even adults. Truly, he admired the girl's strength more and more by the day.
END OF FLASHBACK
Once again, Dumbledore marveled at the kind of power she had mastered in her world. She had demonstrated a few for him. Every time she had, he had felt her aura, bathing everything around her in a light, warm breeze… Her control over her powers was amazing. She could control fire, water and the wind without a wand.
But she needed one to do magic, and honestly speaking, he had been quite relieved to see that. He remembered when he had offered to go to Diagon Alley to get one with her. She had politely declined, saying she and her brother were used to doing things on their own. Her answer was so similar from the one he had gotten from a certain orphan a few years before and yet so different, for he could clearly tell that, where Tom Riddle did not want to be bothered by Dumbledore, the girl's first concern seemed be not to bother Dumbledore any more than she did – or thought she did, really.
He had told her about the war going on, and she had proposed her help to cure the wounded. After all, this was what her family was specialized in. He had declined her offer, only to be treated like a child "Professor, I know you believe a seventeen years old girl should not see the horrors of war, but those I have already seen during my journey. If it is my ability to cure wounds that even your most gifted healers could not cure, I suggest you let me have a try, for you do not the knowledge my clan has gathered. Maybe, what your magic cannot fight back, mine can. Do not let people die on prejudices, Professor." She had told him with that calm tone he had learned to recognize as her greatest strength of persuasion.
And he had let her try. He had suggested she tried to cure a wound that had been inflicted on an auror by one of Grindelwald's werewolf followers. As he was not in his wolf form, the bite had not contaminated him, but he had been a bit… funny ever since. She had simply taken out a bit of parchment, traced characters he could not read on it with her blood (he had winced at that) and muttered unintelligible words for about 20 minutes. The man's wound had become surrounded by a shield of light that had an orange tingle to it, and emitted the exact same feeling as the girl's aura. The wound had started oozing a black, thick fluid, but at the contact of the air, the fluid would immediately evaporate from the skin and appear on the parchment, as if the orange shield of light was acting as a connection between the wound and parchment. It then blend with the blood. As soon as the dark fluid had stopped oozing, she had conjured up a flame und burnt the parchment down to ashes. The light shield had remained in place however and bits of flesh seemed to form in it, only to knit themselves on the auror's scar. This only took a few minutes. When she finally retrieved the light shield, the auror's arm where he had been bitten did not show the slightest sign of ever having been harmed.
- Done! She had exclaimed. It's as if you had never been bitten, trust my word, she beamed at the auror, who had thanked her profusely, while glancing at Dumbledore as if to ask who the girl was.
On their way back, neither had spoken.
"- You know Professor, if you asked me how it worked, I would be happy to tell you.
She smiled that serene smile at him. He simply beamed back at her:
- I would certainly be interested to hear that.
- Well, the characters I write on the parchment act like what you call a spell. It transforms the remains of the curse in this dark, corrosive fluid that you have seen. The light shield drains it from the body and transfers it immediately to the parchment, where the blood and the curse fight. If the blood is stronger, then it absorbs the dark curse. The flames purify the –blending should I say? Anyways, after that, well it is just as simple as treating a normal wound.
- Does it work with anyone's blood?
The girl paused to ponder.
- I believe not. It is my family that invented this, and I think only the blood of a Mibu will do the trick."
Dumbledore wondered whether she would be able to use the same technique on a full werewolf… He would need to find out.