I dont know alot about heat tape with plastic tubs however for your 3 rd question i would use aluminum tape, not normal tape. If you do attach the heat tape to the plastic tub, make sure the plastic is safe to be heated since some plastics give off fumes when heated (these fumes are potentially quite dangerous to your snake) i do see alot of breeders using heat tape with tubs however, they put the heat tape on the surface that the tub is standing on so that they can take the tubs off of the surface and take it somewhere else (for cleaning or taking snake out) without having to worry about the heat tape getting caught in anything or getting wet.