Gosh I have so much headcanon for him, because Marvel will never fill it in for me.
Julian's powers didn't all manifest all at once, but instead in fits and starts. He had headaches for a while because his mutation was, quite literally, rewriting how he perceives the world, and things would break around him. His parents initially thought that he was clumsy because he'd also hit a growth spurt, but his mother suspected that there was something else as well, because Age of X tells me that she carries the mutant gene as well, even if it's not expressed in her case. Eventually he was trying to catch something that he'd dropped (legitimately, even) and he levitated it instead. He stared at it in wonder, going "holy shit what" and then it exploded. Needless to say, his parents were not really kept in the dark about his powers for very long.
Part of his mutation is exceptionally good spatial awareness. This is how he can fly long distances without getting lost; he can keep track of where he is at any given time. He wasn't so great at this at first but he's gotten a lot better over time, which has correlated with his ability to do fine-control telekinesis/psychokinesis.
While Julian says that he was sent to Xavier's because he refused to hide his powers, I suspect it was more that he couldn't because he didn't have that good control over them, and he refused to be contrite about it. It's more badass to say that he refused, though, which is why he says it.
At least once during sex he has thrown the headboard through the wall. IT'S A THING THAT COULD HAPPEN TO ANYONE. :'(
In Legacy, it's come out that Julian has recently become hypersensitive to his surroundings, picking up the molecular structure of everything around him - though it's not a continuous thing. It's a natural evolution of his powers, and I assume that until he gains control over when he is able to turn that awareness on or off, he has times when it switches on without any input from him. He just goes into his room, turns all the lights off and shoves a pillow over his head so that he can't hear or see anything, if it lasts for longer than a few minutes. He pretends it's not happening. I'm sure everyone is fooled.
Whenever playing video games, he has to unlock all of the achievements. It's how he knows he's won the game properly. Everyone else just rolls their eyes because there's competitiveness and then there's JULIAN HOW MANY TIMES ARE YOU GOING TO DO THAT MISSION.
His best subjects at school were maths and science because he can see how those tie into his powerset.
The first time he met Cess, he hit on her. They laugh about this later because really, Julian, what were you thinking?
He keeps meaning to get his hair cut but never gets around to it.
He has moments where he realises that he forgets what certain things feel like to touch. He can tell you approximately how much something weighs and how much telekinetic force he needs to manipulate it, but if someone asked him what it felt like to touch he wouldn't be able to answer, even if he had touched it before losing his hands.
He isn't sure that the older mutants actually know his given name. On the one hand, he doesn't mind because Julian Keller got disowned whereas Hellion is a mutant in training, but on the other, it's kind of I WAS YOUR STUDENT :|
He misses Beast.
He either has PTSD or depression; I've never been too fussed as to which one. Could be both, even! He definitely has some kind of adjustment disorder given how he speaks about his disability.
He has definitely had sex dreams of at least 85% of the mutants he has met, regardless of gender.
Leading from an earlier point, dreaming of falling freaks Julian out a lot because he can't tell how far or fast he is falling and it is disturbing. He'd rather know than ... not.
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