Up front: RMV is the public transportation provider in and around Frankfurt.
There is a detail map which shows the public transport zones superimposed on the stations and public transport lines in pale violet. Here's an index of all network plans of the RMV. Sometimes the Zone boundary is depicted as polygon instead of a boundary line - that's to mark areas where stations can be accessed with tickets from any adjacent zone, just like in a transfer area.
Besides just looking at the map, you can always find out about the involved zones by asking the official RMV tool, the Tarifauskunft. Here you can enter the stations you're starting from and going to and it'll tell you which zones are important in the relation and which Preisstufe, the tariff, of each type of ticket is needed to cover the fare.
So for going from Frankfurt Flughafen Regionalbahnhof to Mainz Hauptbahnhof you're looking at a single fare ticket of Preisstufe 4, involving the zones 5090 for the airport and 6500 for Mainz center. You can also choose from several types of time-based tickets, which are also valid for a set of zones beyond the chosen relation.
In that view, you can also see that there are extension tickets for several types of time-based tickets, called Anschlussfahrkarte. You can buy these if your base ticket, e.g. a ticket valid for an entire month, is not valid for the relevant zones, to extend the validity into these.
That said, the area covered by the RMV is huge. It's basically the entire metropol region around Frankfurt, covering multiple big cities. This means it's hard to digest the entire system from afar. When I go by RMV once a year, I always find it the easiest to enter my destination at a ticket machine and then just select the time validity I need for that relation. The machine takes care of the correct ticket configuration. If you spend a longer time in Frankfurt, consider investing in a time-based ticket with a validity covering all the zones you're going to regularly. When in doubt, go to a service desk, they are prepared to deal with complicated requests, too, and generally are friendly.
About the discounts, I only know about a special offer called the Frankfurt Card which is a 1 or 2 day ticket valid for all Frankfurt zones (50*) offering some discounts in tourist attractions (20% off sightseeing tours, 50% off museums, freebies in some places).