I think it's nice to establish a the general concept of the project before getting into the real nitty-gritty of rules, which will need to be adapted depending on circumstances like how many writers we get, how we decide the tournament should work in-universe, etcetera. Even then, most of these are pretty easy answers which
@Anon_Y_Mousse covered pretty well. But I'll also give my thoughts on the things you and some other people brought up.
POV
I think going for third person would be best. Jumping between first person viewpoints every chapter might be kind of hard to follow, and given that this is a story that will naturally have a lot of characters with their own individual goals, the ability of a writer to tackle the inner thoughts of multiple characters at once (something allowed by third person writing, but not first person so much) will probably be pretty important. First person could be good for giving each individual contestant their own "voice," but I just think third person allows for more versatility in how things are presented.
Obviously we wouldn't do second person, lol. I'm also not saying we
have to do it third person. Just putting my vote in for that.
Deadlines
Probably something like a week and a half, maybe two weeks for each fight people need to write. I think that'd be enough for anyone invested in the project.
Pairing Authors
I'd assume we'd be doing a random draw for the first round of fights, then each one after that is decided by however we decide the tournament/series of fights progresses in the story.
Dropouts
The person who doesn't drop out wins by default, but still needs to write their own side of the story. Simple as that really. I guess if we get a double drop out, we'd just have some other writer tackle that fight and decide which character wins by coin flip? That scenario is something we'd need to address after it happens.
Art
If someone wants to make art, sure, they can go ahead and implement art if they want. But they still need to get their chapter out by the deadline. That's really what matters.
Word Limits / Maximums
I think there should be something like a 500-ish word limit for the introductory chapter someone writes for their submission. Aside from that, fights can be as long or as short as the writer wants. Remember, how this will work is that two writers will each write their own version of the same fight, it'll be released as a single chapter, then the audience votes on a poll for which fight they want to take as the legitimate continuation of the story. I think allowing flexibility in length will also allow more creativity on the author's end.
Genre
I think this is the reason why we need to address some lore right off the bat, actually. Again, we should keep things loose to promote creativity, but we also need to have a defined setting at the end of the day. Personally, I think we should just restrict it to a general "fantasy" theme (if we're going with fantasy) and not flesh out the setting to the point where people feel constrained by it