2019 Update: The Bundestag made a clarification in August 2018, in which they explicitly stated that a level of B1 suffices for the "ausreichende Kenntnisse derdeutschen Sprache" specified in § 10 Abs. 1 S. 1 Nr. 6 Staatsangehörigkeitsgesetz (StAG).
It also mentioned that this requirement doesn't necessarily explicitly refer to the Goethe Institut B1 ...
Yes, the documents for the Anmeldung in Berlin are available on Berlin.de. You can find the original and an English translation here.
You will also need to bring the Einzugsbestätigung des Wohnungsgebers (or Wohnungsgeberbestätigung, or Vermieterbescheinigung), and valid ID document like your passport.
After your Anmeldung appointment, you will get a ...
1) yes, wissenschaftlicher Mitarbeiter (scientific Assistant) is an employment activity
2) yes, City and Postal Code of the Institution is fine (they want to know which Foreigners Office will be responsible for you, which that information supplies)
3) yes, but they must be covered by insurance between entry until the first day of employment, but the ...
If you have a job offer now, you should apply.
Since, I assume, you haven't been working for 24 months job approval by the Job Center must be made
not sure if this applies if the 24 months have been fulfilled in another country
The start date of the contract should be known
and if the training time in Switzerland is within the contract period
If you are out of Germany at a stretch for more than 180 days, your card becomes invalid i.e(180days+1day) or if you de-register from Germany your card becomes invalid immediately. This is what I have been told.
And with EU blue card its one year.
You need to ask the corresponding Ausländerbehörde (before trying to enter Germany). A good idea would be to mention some personal issues that were the reason for you to leave Germany (because it could be a official reason to avoid the expiration of you residence permit, please see details here and here). Actually, you should have asked them before leaving ...
Go to Ausländerbehörde
In order to apply for permanent residence permit, you should be able to fund yourself. If you will quit your job before applying, how do you fund yourself then? (First after you will get a permanent residence permit, you might become eligible for social help, etc.).
P.S. I'm not a lawyer.
My answer may come too late, but still relevant for the people in the similar situation. In general such changes should be possible, but depends on current residence permit and how long one have been in Germany with that residence permit.
There is a nice overview of possible changes of the purpose of residence provided by Federal Office for Migration and ...
Probably my answer becomes too late, but this is a great question, so:
I would suggest that you do not even need two residence permits, rather you can study in both countries under one residence permit, if you satisfy the specific requirements of the European directive on researchers and students, which allows you to live and study in multiple EU countries ...