Hey man, welcome to the board.
Leader of Team GAME
This is something that's decided once the character is approved, you put him on a team with other peoples characters and you don't decide now that he'll be the leader.
He has white spiky hair with black frosted tips
That's...pretty much the exact opposite of how frosted tips work. Is his hair bleached? White hair isn't exactly standard.
black eyes
Why? Why would he have black eyes?
He is about 6,3 and weighs 113 lbs
This is extremely unhealthy, very underweight. That's what I'd expect from a cancer patient in chemo, not someone at the peak of their physical ability. I recommend you look up a height/weight chart to see what's healthy and what isn't.
His body is one like an assassins so he's ready for anything
This doesn't really mean anything, what is an assassins body like? How does that make him ready for anything? I'd just cut it
15 years where he was trained by his father to become an assassin
Ugh, another assassin. Afaik there's nothing actually in the rules against it, but just know that it's been done to death and will earn you a shitty reputation as generally they're written really poorly, so regardless of how good of a writer you actually are, there's a stigma.
So his father trained him, is his dad an assassin too? Why do they live in a small town then, where I'm assuming there would be relatively few assassinations and where everyone would recognize him.
a fury that unlocked his semblance which he used to destroy his hometown.
Why the hell would he destroy an entire town, instead of the Grimm that attacked. Also, a character powerful enough to destroy towns isn't going to be passed as a first year.
He stumbled upon the headmaster of Shade Academy and was accepted in where he was put into team GAME
How soon was this after the town destruction? Are you saying that the headmaster saw a vicious, horrible murderer and thought "Hey, let me bring this guy into my school full of children." That makes no sense.
semblance allows him to control the powers of Yin and Yang itself
Nope. This isn't allowed.
Primary Form: a light weighted katana that can be powered up with fire dust he keeps it in a sheathe on his back wherever he goes.
Secondary Form: a 40k Bolter that uses Shuriken as ammunition he can power up the shuriken with steam and wind dust.
Dust Functions: Wherever Greyson is he can use any of his dust elements but in some places their functions work better than others.
Fire katana seems okay, though once again pretty overdone. In the dust section you need to say what function the dust actually has "makes the blade covered in flames" for example.
For the secondary form, afaik you can't just say a '40k Bolter' as that's ripping off something else. Also shurikens are a horrible ammo, how are they stored? How many does he have? How does the gun actually fire shurikens? And how the hell does a katana turn into a gun that fires shurikens? You need to at least somewhat describe the transition. I'd just scrap the entire secondary form, every single piece of it needs serious revision.