they would have to show evidence
Yes, that’s why they only ban you with an evidence, and they can provide any evidence of any person banned when they want. That’s why you need a proof to ban someone
If it violates the games ToS, they can ban you.
They can, but if they do they obviously have an evidence, they just can’t ban someone basing on presumptions. And if they ban you with no reason, you can go to the court