Help with train travel questions

These sites should be all you need -

German bahn

The Man in Seat 61

If you know your dates of travel, the advance purchase ticket prices are usually significantly cheaper than a rail pass.

That's a lot of train riding. Trains are not always pleasurable experiences, and I limit myself to 3 1/2 hours on them.

Don't forget that European Budget Airlines can get you anywhere on the continent really, really cheap--and fast too.

I, too, recommend The Man in Seat 61 for information. I love the train and this sounds like a great trip to me. The nice thing about the train is it is relaxing and you can see the landscape as you travel and relax, something that can't be done from a plane. You'll just need to compare the prices of per trip to the cost of a pass to see which is more economical for this trip.

Using www.bahn.com, don't worry too much about the exact date. Train schedules don't vary all that much. Use it to get an idea of the times and number of transfers. Don't bother with any kind of railpass.
Munich to Rothenburg can be done with all regional trains using a Bayern ticket.
Rothenburg to Amsterdam is 7 to 8 hours, but I don't see flying as a better alternative as it is still about 3 hours by train to either Munich or Frankfurt airports.
Amsterdam to London could be done rather quicker by air. Look at CityJet to London City airport.

Amsterdam to London - Thalys to Brussels - change to Eurostar to London 4:40 travel time

book tickets here

None of your routes make sense to fly by the time you add getting to/from airports and the 2 hr pre-flight time.

If you get the feeling that Germans are traveling by seeing crowded trains, do yourself a favor and reserve seats. We were in Germany/Austria from July 6-18 and got on more than one overcrowded train. For 10 Euros, we booked 2 seats that are guaranteed for us--even with any type of pass, you are not guaranteed a seat on the train (say you want to go from A to B, then book the seats on the train you want, at the time you want). DB offices in train stations can help you do that--easy peasy. Germans like to get out and travel on weekends so trains are full from Friday-Sunday. I stood up from Stuttgart to Heidelberg, but I was on the train. From then on, we reserved seats. Also, download the Smartphone app for the DB. It can really help you out when planning trips of any kind. I became pretty proficient using the app for planning travel times. Plus, when you know your train travel times, it is easy to say "book my seats on these trains" at the DB offices.

I wouldn't call it a "lot" of train riding. But the most economical way from Amsterdam to London is to fly. See www.skyscanner.com, for instance. From Amsterdam to Schiphol airport is one of the easiest airport connections possible - 15 minutes by frequent local train. You'll have a choice of London airports, including the closer-in London City airport.

So far you have mentioned only two train travel days within Germany and a German Rail Pass starts at three days (about $235 for a single adult, without twin or youth discount), which may be more than you need.