What functions are in the ROM of an Android phone?
Well, the OS is in the ROM, to start with.

You're suffering from a terminology problem: "ROM"s these days are all typically Flash memory, which is erasable and rewritable, but not byte-by-byte. So the OS may even live in the same physical ICs as the 'main' phone memory.

Basically, custom ROMs can enhance/modify/break EVERY aspect of your phone's operation. There is a separate 'radio rom' which includes the low-level drivers for the wifi/gps/3g/gsm/bluetooth functions, and these typically aren't 'customised' but you may still find newer versions available that can improve certain aspects of your phone.