You are correct in your first question - each router must be running the same routing protocol (RIP, in this case) in order to send/receive the updates.
You can configure more than one protocol per router, but there are disadvantages:
1) complexity - it becomes more of a burden to manage to some extent
2) resources - each routing protocol consumes resources (CPU, memory) of the appliance
3) overhead - each protocol is now consuming some amount of bandwidth on your links
In the end, the protocol with the lowest administrative distance is going to win, anyway.
Another thing to remember: RIPv2 auto-summarizes to classful boundaries by default. Depending on your addressing scheme, you may want to add the "no auto-summary" command to your RIP configuration.
Good luck!