hey there, yes you can just break them off in pieces, not really exact science, but with practice can get the piece you want pretty close to how you want most of the time, and as to survival, well thats a waiting game, mount it and give it the time needed to heal in a grow-out tank, or your display if you choose, and it if healthy should have some new growth visible within 2-3 weeks, give or take depending on exact conditions of aquarium its in, and if there is new growth and no bleaching then its a good frag evidently, and sell it or trade it off time.
have a good one.