Can I salvage my leaky ceramic shower stall?

It sounds to me like you need to reconstruct at least the floor, and probably the entire shower. If water’s getting through the existing shower pan, it’s putting the integrity of the underlying floor at risk. While you could reconstruct the floor in the traditional way, with mortar, you’ll get durable results much more easily and quickly if you use a product called Kerdi-Shower-ST. It’s a ready-made shower base made from rigid foam by a company called Schluter. You can find it at most home-improvement outlets. The pan is cut to fit, and sloped for drainage. Despite the fact that it’s made of foam, this product is ideal as a base for ceramic tiles. If you do decide to gut your entire shower and start from scratch, the Kerdi-Shower-ST is designed to work in conjunction with related components for building the waterproof walls of a shower.