Your "hard parameters" as I understand them.
- You will fly Singapore > FRA > Singapore.
- You will travel by train.
- you have maybe 14-16 days for sightseeing (exact number not yet completely clear)
Your wishes... NOT etched in stone, but penciled in at this point:
- Rothenburg, Auschwitz, Berlin, Munich, Krakow, "Czech" (which everyone here is assuming to mean PRAGUE.)
Your goal: to understand the history and culture.
The consensus so far: Your trip is too rushed.
Here's my contribution... Listen to the consensus.
1) DROP 1 or more of your wish-list destinations. I completely agree with the idea of dropping Auschwitz/Krakow, not because of border controls, but simply because, as others have stated, you can visit Dachau from Munich. The fact that one person you have worked with recommended Auschwitz does not outweight the recommendations that others have given you for Dachau. Krakow is on your BUCKET list, right? So are you almost ready to "kick the bucket"??? I hope not. As Rick Steves has advised, travel with the understanding that you will be back again sometime later.
2) Ignore suggestions for ADDITIONAL destinations. If you can create a travel plan for Rothenburg, Munich, Prague, and Berlin, that alone will be MORE than challenging in the time you have. If you cannot, drop a second destination. It is presumptuous to think you can really understand the history and culture of even ONE country in two weeks. But there is no doubt in my mind that if are able to spend at least 4 nights in the major cities (Munich, Berlin, and Prague) then you will understand more about each of those places than you will if you try to also include time in Krakow, Frankfurt, the Romantic Road, Salzburg, Berchtesgaden...
3) You are struggling to get a ticket to Rothenburg right after your flight. Try this.
Flight arrives FRA 6:30 am (maybe.)
Pre-purchase a saver fare ticket for FRA > Rothenburg which uses ICE trains from FRA to Frankfurt Hbf, then REGIONAL TRAINS from Frankfurt Hbf > Rothenburg.
Here is a sample schedule I just reviewed: 9:02 - 12:51, sample date Sept. 23
- ICE from FRA 9:02, ar Frankfurt Hbf 9:13; change trains
RE train from Frankfurt Hbf 9:30, changes of train in Würzburg and Steinach as usual; ar. Rothenburg 12:51
Price = €23.99 saver fare. (To find this schedule and saver fare ticket, you might need to specify Frankfurt Hbf as a stopover and also to specify Long-Distance trains only for the FRA > Frankfurt Hbf segment, local transport only for the Frankfurt Hbf > Rothenburg segment.
Regional train travel in Germany is 100% flexible; only the ICE train time is fixed. So if your flight is late and you miss the 9:02 train, it's no big deal. You simply purchase a standard one-way ticket to get to Frankfurt Hbf (€15.90 on any ICE train, or €6.60 on the S-Bahn train.) And then you travel on some later regional train sequence using your original saver fare ticket, which is still valid for ANY of the regional trains to Rothenburg that same day. Rothenburg is not a short trip from FRA airport. But Rothenburg and FRA were your choices, so...
I would spend no more than 2 nights in Rothenburg. Then 4 each in Munich, Prague, and Berlin. Then ONE night at FRA airport before your final flight - you don't have time to understand Frankfurt proper or the street people by the train station and have no stated interest in seeing Frankfurt anyway, and you should encounter no druggies around an airport hotel. I am not sure you have 15 nights. Maybe you have 16. Then you have one additional night for Berlin.