Granite in Shower, Need Cleaning Advice!

I just moved into a condo and am renting from the owner. The shower is mostly rock/stone tile, but has a granite shelf. One question I have is what can I use to clean this shower that won't damage the granite? The other question is that I have used the shelf to hold soap/shampoo/conditioner/etc. and it seems to be darkening the granite in certain spots (the granite is a white/gray/black mix). Is there any way I can clean these spots or remove them? Please help, I know nothing about granite!