Ok, here's the direction I could see this game going:
1) Take out the "random weapon firing" mechanic and replace it with weapons randomly falling from the sky that you can pick up.
2) Extend the arena, and maybe even add several arenas with different pitfalls to avoid.
3) Make the players only slide when they've been hit, otherwise, make their controls sharp and snappy. The slipping around is not fun. I kind of like it, but my girlfriend hated it (Also, I've made a multiplayer game similar to this before about fighting on ice, and a big reason I gave up on the project was because people consistently hated sliddy player movement).
4) Add controller support and up to 4 players (this will necessity a 4x or 5x increase in the size of the map AT LEAST). With controller support, allow the players to aim their weapon with the right joy stick, and fire with the right trigger.
5) Instead of "life", do a smash brothers style "percentage" system, where the amount of knock back a player experiences is multiplied by the "percentage" of damage they have accumulated. Give the players some number of lives. When they fall off the map, they lose a life. No more lives, and you're out. Basically, turn the game into top down smash brothers.
That's exactly the direction I would take this game. I don't think this is necessarily the "correct" direction to take this game, but having worked on a EXTREMELY similar project before, that's the direction I was going to take it before I scrapped the project (because local co-op doesn't sell, and online multiplayer is hard to implement). Good luck my friend. I hope at least some of these ideas help you decide where to take the project next.