Try Action Handgun or Speed Handgun - or even Cowboy Action. No static firing positions there - especially so in Action, which is a course of fire not unlike you see in military training from which it is derived. Lots of running, diving, ducking, shooting from cover and so on.
Haha, I like action shooting, but I wouldn't dare try diving and rolling. I'll admit, that's probably a situation where I'd end up shooting myself in the head!
Meh. As long as the weapon is holstered and fully functional in terms of safety etc you should be fine. Soldiers and police have to do it all the time and the number who get shot by AD in those situations is so small as to be statistically irrelevant. Were that not so, the US gun makers would be sued from now until Doomsday for starters!
I watched someone do an Action course in the US with a pair of fully auto Glock 18's with no trouble.