Most faucets just screw on. Throw a wrench to it and give it a push. Righty/tighty, lefty/loosey. It should pop free I had this problem and noticed the underside of faucet was allowing water to travel back to and down the wall. I picked a new one up at the local hardware ana no problem since. Make sure you use plumbers tape on threads when reinstalling, and get some tub and tile caulk for the gap you mentioned. Follow the directions on the tube. (caulk)