What I'm really hoping the rules are of this arena are that I can challenge someone to a fight and rank up depending on my wins. Correct me if I'm wrong. Just tell me, do I need a character sheet? Because I am so ready for a good fight.
I think what you're looking for is a ranked match, which I don't personally do, but it definitely exists here. I'm pretty sure some of the regulars here will take you up on it. I'm not actually sure if there's a universal rule involving having character sheets, but generally speaking I think it's a good idea to have them -- without a character sheet, people could just pull whatever bullshit they wanted out of nowhere.