How do we get to Rothenberg from Munich by train and do we need advance reservations in December?
Journey planner: https://int.bahn.de/en
Looks like there are regional train connections every 2 hours at about 35 minutes past, i.e., 9:35, 11:35, etc. They take just over 3 hours with one or two changes. You will always have a change at Steinach. Some regional connections also have a change at Treuchtlingen, some don't.
The train from Munich starts at the Hbf, so if you get there early, you shouldn't have any problem getting a seat, and if you get one of the one change connections you only have to worry about a seat on the shuttle up to Rothenburg.
Regional trains do not require (or offer) reservations. There are connections starting with a long distance train (ICE) from Munich Hbf to Augsburg or Nürnberg. They offer but don't require reservations. However, those connections have more changes and use regional trains from the first change stations, so there is not much advantage for using them.