Wow, I really forgot to post the result here!
Three weeks ago I finally lubricated the chain, and then called the shop. They fetched the motorbike, changed brake fluid and coolant, checked that all the things I did were OK. Then I got the TÜV certification.
…and since then there was always bad weather when I had time to ride, so all I did was ride her home…
But hey, I have a working motorbike again! 