Welcome to the forum.
What's your planned arrival time at MUC? Even if it's early, I'd probably not think of Day 1 not as a sightseeing day. Consider possible flight delays, baggage + security waits, the 45-minute transfer into Munich, then the associated logistics of getting settled, and the potential for jet lag and fatigue from the transatlantic red-eye flight you just stepped off. That leaves 12 full days for seeing things in the 10 different destination cities/towns you mention. But those days are also full of transportation hours, which further subtract from your boots-on-the-ground time. Very little time is available for Munich. Your day trip to Füssen will require nearly 5 hours of transport if you're there for Neuschwanstein. The logistics of 7 different overnight spots subtracts quality time as well.
The streamlined itinerary below reduces the number of overnight stops and lengthens most of them. It also sticks largely to the main railway from Munich to Berlin. Some detours from the stops I name on this route, including Rothenburg, would be optional, so that you have more choices and fewer absolute deadlines for hopping on the next train. I've dropped Füssen and Dresden.
Night 1: Freising (super close to MUC, 11 min. by train; walk, eat, drink, relax in this comfy small town, adjust your inner clocks; try to stay up until at least 8 pm.)
Nights 2-5: Nuremberg
Nuremberg is a very fine choice and a great base for taking short outings.
Day 2: Freising > MUNICH (25 min's, direct early morning train.) Fully rested, you arrive in Munich, drop bags in a station locker, and carry out your sightseeing plans there. Munich > NUREMBERG (1.75 hrs, direct RE train in evening, or faster by ICE train.)
Day 3: 1 full day in Nuremberg
Days 4, 5: More time in Nuremberg? Or... outings by regional train to Rothenburg (1.25 hrs.) to the beautiful old-world art/wine town of Iphofen (45 min's) to Bad Windsheim's Franconian Open Air museum (55 min.) or to Würzburg ( 1 hr. 10 min's.) You don't have to decide now - these can all be done on the fly. Super-cheap and super-flexible day passes (VGN Tagesticket Plus) are available at ticket machines for these outings (but use the Bayern Ticket for Würzburg.)
Nights 6-8: Erfurt
Day 6 Nuremberg > (Bamberg) > ERFURT 1.3 hours by ICE train (or 3.75 hrs by regional train, ugh)
Stopover option en route to Erfurt: Bamberg, just 30-45 minutes out of Nuremberg, on the same railway line as Erfurt. It's a UNESCO World Heritage site for its medieval city center and worth at least half a day. Stow bags in a station locker while you visit.
Days 7 & 8 for Erfurt and Eisenach/Wartburg outing. You didn't visit Bamberg on Day 6? Maybe you'd find time for a 48-minute train outing through beautiful countryside to Mühlhausen.
Night 9: Wittenberg
Day 9: Wake up in Erfurt; catch morning train to LEIPZIG, drop bags in locker, full day for sightseeing. Continue by train to Lutherstadt Wittenberg in the pm.
Nights 10-13: Berlin
Day 10: Wake up in Lutherstadt Wittenberg (nice town to overnight in, IMHO) for a full day of sightseeing. Continue by train in pm to Berlin.
Days 11-13: in Berlin only
The daytime stopovers I suggested (Munich, Bamberg, Leipzig) might require specified stopover periods if you plan to use the ICE or other high-speed trains with saver fare tickets.