If not just start a barroom brawl
Ask them but I would say the answer is no. They don't want to be sued because you got your lights knocked out, ended up in the hospital, and then off to physical rehab because you needed to be taught the science and art of eating soup through a straw because you have no teeth. I hope you're not considering such a stunt just to try and impress some girl.
Probably not, but they might provided that you signed a statement saying that you won't sue them no matter what happens to you in the fight.
Why not, if you train hard enough to get your skills up at competition level.
Many boxing gyms, like Title Boxing, don't allow sparring. Call them in advance and ask.
Sure but you Would need to put in some work first in the gym(practice)