"Backyard" MMA regarding legal issues?

There are some other questions that come in to play. Are you paying the fighters? Is the audience paying you for their seat? If the answer is yes to either of these, then you are conducting business like a promoter. Promoting without a license is illegal. If it is just a bunch of guys getting together on privet property to start a sort of fight club, and no money is exchanged with anyone I believe your safe. The best thing to do is to contact the athletic commission of the state you live in and ask if what you want to do is legal.

No, you'd be liable for anything that occurred. It's also illegal.