How do I clean old paint that is peeling off the walls and floor of painted cement block shower? What products should be used to repaint?

The peeling is likely due to moisture behind and inside the block. Cement block was never intended to be a shower liner. You might want to consider installing a ready made fiberglass liner that can be glued to clean block. The drain connection is an open question because I don't know what makes up your current drain. It might just be an old floor drain that someone center a shower over.