I'll focus my remarks on Berlin especially pertaining to your historical aims there. I did too my first time to Germany which included (west)Berlin, obviously.
Fantastic that 7 nights are being set aside to track down "historical sights" in Berlin. One needs at least that much time to devote to seeing these sights seriously. Keep in mind that as a general rule :historical Berlin " is east of the Brandenburg Gate and adjacent Pariser Platz.
Yes, historical sites are to be found in the western side of Berlin such as those in Spandau, Charlottenburg, Wannsee , Steglitz, etc but these area until 1920 suburbs, likewise in the eastern Berlin, such as Koepenick, Karlshorst.
First of all, Berlin is huge, going from the western end, say Spandau to the eastern end, therabouts, west to east laterally on the S-Bahn takes at least one hour. If you want to do this, I suggest taking the S-3 (Direction: Eckner).
Eastern Berlin offers numerous cultural and historical sites, it all depends on the level of your interest in pursuing them, such as the house / museum of that great dramatist, writer of the German Enlightenment, G. Lessing. Aside from cultural sites, if you want those connected with Prussian-German history, they're there too.