Can I remove ONE piece of ceramic floor tile without damaging the rest of the floor?
This is pretty difficult and best left to a professional. However, if youre going to try, remember a couple of key points: be sure you have a very strong color match, as one tile out of color will really draw attention to itself. Also, use a small chisel, and chip the old tile out. Dont take any big whacks at it. Be patient. Be sure to remove ALL the grout for that piece of tile, while NOT removing any grout from underneath any of the surrounding pieces. You can then grout the empty area right up to the other four pieces, and lay in the new piece.
