You can't have one character with every ability, no.
Level cap is 20, one ability per level (starting from 0, so you get 20 abilities).
But there are 58 abilities in-game.
And it's designed for all systems, not just one - the dev team have focused on making the game as good on every platform.
EDIT: You get 10 characters though, so you should be able to cover everything easily enough