But still, you didn't thought about one thing. What if a legit player picks up a gun that the hacker spawned? He can get banned for that.
As for the super jump thing, I didn't test but am pretty sure it wont work.
EDIT: That is if you are relying on 1 API. But if you really want to add that then you will have to check for if he is currently jumping and if his location's distance from ground is too high by a collison trace to ground.