9 nights in southern Germany by train--need itinerary advice

"Day 1 arrive in Frankfurt 6am, train to Baden-Baden, stay overnight in either Baden-Baden or Freiburg...Day 2 stay somewhere in Black Forest, hiking?"

Hiking in the Black Forest in March is iffy at best. Rick Steves pushes Baden-Baden and Freiburg but neither is in the Black Forest, really; B-B is mostly about spas and casinos and Freiburg is nice but not exceptional. I think you could skip the BF part and see it at a better time of year some other time.

In Füssen, if by "castles" you mean Neuschwanstein and Hohenschwangau, you won't be seeing real castles. N'stein resembles one but is in fact an opulent royal residence built in the late 19th century with a fake castle facade. Both places are officially palaces.

So my suggestion is from Frankfurt airport to travel about 1 hour to the northwest and spend your first 2 nights in the Middle Rhine Valley, an official UNESCO World Heritage site, where you can see and tour some real medieval castles and also see some of the half-timbered architecture in the old-world towns there (very similar to what you'd find in the small Black Forest towns.) Then continue to Würzburg, etc.

Train from FRA to Bacharach: €23/2 adults on the regional trains (buy RMV ticket at FRA station ticket machine.)
Nice towns nearby: Oberwesel (5 minutes by train); St. Goar and Rheinfels Castle (10 min.); Braubach and Marksburg Castle. To reach Braubach, cross the river using the St. Goar ferry and take the train 20 minutes north to Braubach.

The Middle Rhine region is very good for hiking just in case the weather cooperates.

Bacharach to Würzburg will take about 3 hours if you pick the better train connections. (The train trips from Frankfurt to Freiburg and then from Freiburg to Rothenburg as you have them planned would require several hours longer because of the long distances involved; seeing the Middle Rhine instead means more feet-on-the-ground time and less expense as well.)

Day 3 train to Wurzburg or Bamberg, maybe stop in Rothenburg on the way?

Easier said than done. Rothenburg is a side track off of a side track, so rail logistics are daunting for a "stop off on way".

You could do worse than camping out in Nuremberg for 4 nights and do day trips to Wuerzburg, Bamberg, and Rothenburg. Train tickets are cheap using the VGN network, Bayern tickets, and other regional discount tickets.

I've been in Baden-Baden, and I wasn't impressed, although I have to admit my preferences are not so much large cities but small towns with scenic appeal. But from Baden-Baden you can get to the German hill called the Merkur, which has some notable hiking. It's just that the town, itself, to me, is not very interesting.

I would prefer to stay in the Black Forest spa town of Bad Herrenalb, which is about a 40 minute streetcar ride out of Karlsruhe, two hours from FRA by ICE and the streetcar. The hills outside of Bad Herrenalb are riddled with hiking trails. I was there in late March and there was no snow and the trails were all open (of course, YMMV). Bad Herenalb also has a spa where you can recover in the warm waters from jet lag or your strenuous hikes.

Iincluding a 3 hour stopover in Rothenburg, the trip from Bad Herrenalb to Würzburg would take 9 hours. With advance purchase, the Saving Fare ticket, including an IC from Karlsruhe to Ansbach, would be as low as 55€.

Day 8 Munich--maybe Kloster Andechs on the way

Getting to Andechs from Füssen by rail is a bit awkward. It'll require one or two changes of train and two to three hours of travel. On the other hand, getting to Andechs from Munich is easy, and well worthwhile. Just take the S8 southwest to the end of the line at Herrsching. From there take a local bus, taxi, or walk three miles or so up the forested footpath. Signs ("Fußweg nach Andechs") direct you to the footpath from the S-Bahn stop, as in this photo, taken on the sidewalk directly in front of the S-Bahn. The yellow-orange building across the street with white columns is the tourist information office.