I spent a few months in Darmstadt. Agree about all the positives you mentioned. One negative I want to add is that relatively few people speak English.
I did the same thing -- a summer in grad school doing research -- but I did think it was a great opportunity to learn German.
Yep, iirc I was not officially "registered" with the uni, but they still opened up free basic german classes if I was interested.
Interesting. On what status (i.e. type of visa) did you go to Germany?
Sorry, I don't remember anymore. It was a scholarship called WISE, but I'm unsure what type of work permit I got, etc. If I can hunt down my old passport I'll check