What functions are in the ROM of an Android phone? I would like to get a clear picture of what is in the ROM vs. what is in the OS. This will help me understand what those custom ROMs are all about.
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.