Ceramic tile salvage can be done with a great deal of patience. Grout removal should be done gently to avoid damaging ceramic tile. The next step will be prying the tile loose from its base. Then clean it up and your ceramic tile reinstallation should go very well.
Install ceramic tile successfully when the tile is laid on a level surface. Floor leveling compounds will help with this. Use drywall finishing tools to get a glass like surface.
Low water pressure problems can be checked easily. Water shut off valves need to be checked indoors and out. Your local water works people can do a bypass check.