#1 -- You can register your team name here.
But I don't think it's an offical site of KCBS. KCBS will let you know if your name has been used before.
#2 -- There's all sorts of tricks to that. Besides the obvious of putting sauce or mop on it. I've heard of people spraying pam, water, beer, etc on the turn in box. A quick shake of accent also helps the meat. I'm sure more experienced guys can chime in here.
#3 -- I'll answer for Phil since he's taking Sharon out to dinner, but we used a combo of the Klose Backyard Chef and Weber Smokey Mountains. Don't let the type of cooker you have stop you. People use every type including home made.