Berto, my friend, you are way too ambitious.

Chill, buddy!
If you want to do a lot of stuff the three car museums would actually fit the bill and still be do-able. There are good connections from Paris direct to Stuttgart, even ICE but also normal IC (unless they have cancelled that because there is the ICE now). There should also be some that leave rather late. I think you said there is a direct train to Munich now from Paris?
In any case, let's lay out an example. Leave Paris to STG in the evening. Stay in Stuttgart (cheaper than Paris and possibly cheaper than MUC) overnight. Enjoy some Maultaschen or Spaetzle for dinner. Yum!!! In the morning visit the MB and Porsche Museums. The Porsche one is breathtaking already from the outside. I drove by there not even three weeks ago and my heart almost stopped. The MB I've only seen on photos but it's very nice, too. You probably need a total time of around 6 hours for both incl. transit. Say you are done by 3pm. Take a train to Munich. Depending on when you arrive and the day of the week you might still be able to cram the BMW museum in there but I wouldn't try. Munich has art museums up the wazoo and they are all centrally located. The BMW museum isn't. So either take in one of their fabulous art museums (the Old Masters are particularly impressive) or just take a stroll to the wonderful city that Munich is. Hang out in a street cafe, practice your German with one of the pretty Dirndls and enjoy a good coffee or beer (obviously). In the evening you might go to a concert or clubbing. The scene is quite good, I hear. The next morning you have Weisswurst und Senf for breakfast and thusly strengthened you can face the BMW museum. If you had more time I could also imagine a visit to Schloss Nymphenburg but you probably need to get rolling back to Frankfurt.
I'd definitely spend the night from 14 to 15 Feb in FRA. You should be at the airport 90 minutes early for an international flight. It is a huge airport and things can go wrong.
Scrap the entire Garmisch, Zugspitze, Freiburg, Nuremberg deal. Too much time spent in transit. Freiburg is one of the most remote corners of Germany in terms of geographical position and thus it is a PITA to even go there, let alone get outta there to catch a flight. NUremberg is nice but not that nice. I'd spend a day in Dusseldorf any day over a day in Nuremberg or Freiburg.
The must see cities in Germany (besides some small medieval places) are in descending order:
1.Berlin
2.Munich
3.Hamburg
4.Dresden
5. ex aequo: STG, Heidelberg, Cologne, Bremen
6. ex aequo: Frankfurt and Dusseldorf though I'd give a slight notch to DUS
Somewhere in there Leipzig might find a place. And Hannover, too. Probably these are on par with Hannover. I might rank all of those at 7. Some people might dispute these also ran positions but hardly anyone is going to dispute the top four; maybe their order but not that those are the top four.
Of the medium and small cities don't forget Weimar (see Goethe again, and Schiller) and Lubeck, Bamberg and Rothenburg, Lindau, Meersburg.
Till