I don't see a problem keeping a pit in an apartment. The only problem would be is, do they allow pitbulls? Some would allow if they're under 30 pounds. When they see a medium-large pit living in their apartment, they'll complain but when it's under 30 pounds, they think its a cutie pie when I walk my dogs, almost everyone who saw them rather tell me my dogs are cute instead of telling me my sons are cute
If you do decide to keep one, get an extra large foldable cage crate. That way the dog could move around and do what he needs to when you're not around, and still have a dry area to lay on. As for exercise equipment, get an E-mill. Nobody will know its for the dog when they see one of those. And for bite work, make a flirt pole with a hide attach to it. That's all you'll need. You could have him as a pet bull and still compete.