"Overpowered" stuff like making anyone believe anything at anytime would be the easiest for a person, but also one of the most selfish superpowers.
You can have ANY SUPERPOWER. What is it, why, and how would you use it?

Yeah, but functionally the "make anyone believe anything" can do pretty much everything telekinesis can (and more).
The only thing the mind control thing can't do is lift objects or something like that... but while lifting objects with your mind would be cool, it's almost never useful.

Here's a funny superpower (I'm trying to think of one that isn't so selfish)
You can grant wishes for anyone, but not for yourself

Not sure what you meant, but thanks?
Just because it offends your sensibilities doesn't make it cheating. You have to make a logical argument for why it's cheating.
One argument you could make, for example, is that even if it's not cheating, it violates the basic spirit of competition, and a rose by any other name, etc.
Another is that if all superpowers were allowed, then games as we know them (like chess) would greatly diminish in popularity, and some may even cease to be played. So even if it's not cheating it would have really negative effects.