"Is there a train pass that you recommend that might be more economical?"
There are two basic TRAIN TYPES in Germany:
Bacharach and Rothenburg are small towns that are served by regional trains only. So every one of your trips within Germany will include one or more regional trains.
For your trips within Germany you have a choice; you can travel between the towns you mention either by... a.) regional train only or b.) long-distance train + regional train (which is a bit faster.)
DAY PASSES can be bought right at the station for the best possible price. They apply to option a.) only.
Here is the D'dorf > Bacharach and Bacharach > Rothenburg day pass option:
https://www.bahn.com/en/view/offers/regional/day-ticket-for-germany.shtml
Here is the Rothenburg > Munich day pass option:
http://www.munich-touristinfo.de/Bavaria-Ticket.htm
Each of the above trips could also be done using long-distance + regional trains (option b.) For this option you need regular train tickets. To save money, purchase a Sparpreis ticket in advance. If you buy later on, you may have to pay the normal fare.
For A'dam > D'dorf you will use long-distance trains and you need this pre-purchased train ticket.
The airport-city day ticket can be bought at Munich station and will get you to the airport
When you use the DB itinerary page to search for train journeys, these tickets normally show up as options automatically if they are available... HOWEVER... to find all the train options for regional trains only (and use the cheap day tickets) you will have to click on the "only local transport" box under connections. That will eliminate all the long-distance trains.