Getting from Munich Airport to Nuremburg

You will need to take the S bahn (commuter train) to the Munich Hauptbahnhof (Hbh). Then there are frequent direct trains to Nuremberg. You can fnd the schedule and prices on the Deutsche bahn website:
https://www.bahn.com/en/view/index.shtml

Since arrival time and length of time needed for passport control and baggage retrieval can have delays, you will have to weigh buying advance discounted tickets online vs the regular price tickets when you get to the train station. If buying in advance, allow several hours before train departure.

Take the SBahn train at the airport to Munich Hauptbahnhof.
At Munich Hauptbahnhof change for trains to Nuremburg.

Thanks for the information.

From there we will need to get;

• From Nuremberg to Fussen.
  
• From Fussen back to Munich.

Nuremberg to Fussen.
Fussen back to Munich

These routes you can search on https://www.bahn.com/en/view/index.shtml.
Go with the train routes that require you to change trains the least amount of times.

I see four train/ticket options for getting from the Munich Airport to Nürnberg.

Full fare ticket: Will cost €126 for 2 P. You can use any train(s) after your arrival. S-Bahn to Munich Hbf, ICE from there to Nürnberg is the fastest (about 2 hours).

Saver Fare ticket: Will cost about €60 for 2 P (for the least expensive version). Same train options as Full Fare, but only for one specific ICE to Nürnberg. If you change your mind about connection time or if your flight arrives late and you miss that ICE, your ticket is worthless.

There are two versions of these ticket. With the €60 version, the Super Saver, the specific ICE is set from the day you purchase your ticket. No exchange or refund. If you change you mind, the ticket is worthless on any other ICE. With the regular
Saver for €12 more for 2P, you can exchange the ticket, by paying a penalty for a voucher, up to the day before arrival. You could still loose you ticket with a late arrival. If you provide a buffer of, say, an hour or two, you might as well take regional trains (below).

Bayern-Ticket and regional trains. A €32 (for 2 P) Bayern-Ticket allows you to use any regional trains that day in Bavaria. You could take the S-Bahn into the Munich Hbf and a fast RE to Nürnberg. Or, you could take an RE from the airport to Regensburg and change there to another RE to Nürnberg. There are other options (see Bahn webpage). Connections would be about 45 min to 2 hours longer.

Rail&Fly: This ticket is like the Full Fare ticket above as far as flexibility and train choice. R&F has to be booked with your airline, and not all airlines book it. Also might not be available after your air tickets have been booked. It cost about €66 for 2P.

As for minimizing train changes, don't be intimidated. Train changes in Germany are far easier than plane changes. Also, the change place is significant. Changing at Munich Hbf involves coming out of the underground S-Bahn station to one of the 26 tracks in the main part of the station. Changing at Regensburg would be easier.

Just to make sure does the German Railpass allow to travel on: ICE, S-Bahn, Regional-Express and Bayerische Regiobahn?

Yes. The German Rail Pass allows you to travel on any of the four. In addition to the ICE, the German Rail Pass is valid on ECs and ICs. Regional passes, such as the Bayern-Ticket, are valid on three, but not on an ICE (or IC/EC).