The terrazzo shower receptor you are describe is constructed of tan and white marble chips cast in portland cement. The surface is ground and polished, then grouted and polished again. It sounds as if some of the grouting has eroded due to the leaky shower head. Incidentally, we recommend repair or replacement of the existing shower faucet prior to repairing the shower pan or any repair you make to the pan will be in vain.
Your question prompted us to contact Florestone Products, a major manufacturer of terrazzo shower receptors. They recommend filling any pitted areas with a white cement grout, provided the pitting is centralized and not extensive. Replacement is recommended if the pitting is extensive. Once you have repaired the pitted area you will want to seal it with a clear silicone sealer designed to repel water.
With respect to your question about cleaning terrazzo, soaps and scrubbing powders containing detergents, water soluble inorganic salts or crystallizing salts should not be used. terrazzo, like any floor surface, is susceptible to staining. Stains should be treated as soon as possible because they are more difficult to remove the longer they have to set. The type of stain should be determined so that the proper remover can be selected. Stain removers fall into two general categories: 1) solvents, such as carbon tetrachloride, which dissolve grease 2) bleaches, such as household ammonia, hydrogen peroxide, acetic acid or lemon juice, which discolor stains. Although it works great on fiberglass tubs, we would recommend against using the turpentine salt mixture in this situation.