SPOILERS FOR CAPTAIN AMERICA: CIVIL WAR!
Didn't think I would be saying this in a movie based on my most detested Marvel event but I loved Captain America: Civil War and Peter and T'Challa were among the best parts! I remember reading one story on archiveofourown taking place after the airport battle in the movie which ended up with Peter calling Black Panther his new favourite superhero but I can't remember. True story though it of course ended up being Tony, when I read that the press saying Spidey would have a bond with a character in the movie I half jokingly thought it might be T'Challa and this is me rolling with the idea. This takes place after the airport battle in the movie so major spoilers ahead!
The biggest battle so far of the Avengers Civil War over the Sokovia Accords happened in a foreign airport and though it resulted in most of the team led by Captain America Steve Rogers got captured, it was actually clear they had won the battle with their goal of Steve and Bucky Barnes the Winter Solider escaping to find the location of HYDRA's secret five Winter Soldiers. Right now most of the team led by Iron Man Tony Stark were recuperation, Tony most likely being chewed out by United States Secretary of the State Thaddeus Ross and James Rhodes or War Machine being injured in the fight.
The youngest hero involved in this battle Peter Park was fixing up the mask of his newest Spider-Man suit given to him by Tony Stark, putting it back on while Tony was having arrangements made to send him home to Queens, New York. Well Peter got hurt but it was nice being able to fight amongst his favourite heroes in the Avengers even though he had to fight half of them, and he only had his powers for about six years. "So you are the so called Spider-Man?" Peter heard a voice and turned around to see T'Challa the de-facto king of Wakanda after the death of his father recently and was wearing his Black Panther suit only with his helmet under his arm.
"Well you're King T'Challa of the isolationist country Wakanda right?" Peter questioned and T'Challa gave a silent nod. "Awesome your highness, you were really cool out there! So you are a superhero king, I made a report about your country for school last week, got a solid A+ on it as well." Peter told him causing T'Challa to raise an eyebrow.
"You are quite young, still in your teens, I presume?" T'Challa asked figuring this kid might still be in high school due to the school report he just mentioned and the fact that he referenced the Empire Strikes Back as an old movie (just because Wakanda was isolationist doesn't mean they did not have TV or movies). This comment made Peter pause for a second in fear not wanting his secret identity to go out.
"I am kind of fifteen years old..." Peter told him and T'Challa lost a bit more respect for Stark for this, enlisting a fifteen year old in this battle? He would be having a talk with Stark about using child soldiers later. From the reflexes and strength he saw him use in action T'Challa would guess that he was probably one of the Inhumans that have popped up recently. T'Challa was actually surprised that most of them he heard about didn't think of trying out to be a superhero like the Avengers but he had bigger problems to deal with.
"Well I have got to go and track down once again the killer of my father." T'Challa told him as he put his helmet back on but his comment made Peter realise something. He told T'Challa to wait and T'Challa decided to humour him a bit for a moment later.
"Your highness, before you go... I am sorry for your father... I had a parental figure in my life that I lost only a few months ago and I almost let my desire for vengeance consume me and I was able to stop myself from making a big mistake. I know I am probably some low commoner whose opinion doesn't matter to a king like you but please just remember what the path of vengeance could lead to and plus would it be something your father would have wanted?" Peter told him and T'Challa took a moment to think over his words. He sighed not helping but to admire the youthful optimistic side that this teen vigilante was showing him. But still he had to settle it by finding Steve and Bucky and whatever would happened next would happen.
"I will take your words into account, you didn't do badly at the airport and you could do real well someday but now I must go and settle things once and for all." T'Challa told him through his helmet as he walked towards the door. "Good luck in your future endeavours Spider-Man and may you unlock the potential to become something amazing." T'Challa told him with one final word before leaving and Peter was thinking over the talk he just had with an actual superhero king!
"The Amazing Spider-Man..." Peter thought thinking it over before deciding it might have a nice ring to it! "Wow I had a conversation with a king of his own country; I just wish I was able to tell Aunt May about this but whatever..." Peter said thinking on what to do now. "Maybe War Machines needs someone to keep him company while he recuperates." Peter said walking about trying to see if he could find where Rhodes was at to get treatment for his injuries. If not maybe he could go and have a talk with the Vision or something, maybe even Tony Stark again...
I know there is one other story here about how young Peter is though it mainly consists of the imprisoned members of Team Cap, I am keeping this as incomplete just in case I want to expand on it.