One more remark before I go to sleep:

When I open Jaxx and it gets stuck on the blue screen I can still click on "view" > "Advanced" > "toggle dev tools" and there an interesting line is listed, saying "show_splash should be removed on app start. Only intro screen will use it (JaxxIntroCreationWalletComponent)"
Now, I have no clue who suggested this and why this line is there, but it might be part of my problem.

I searched a bit on the internet and a show-splash is a fancy but often unneccessary intro to an app, that can cause problems starting the real program. In this case this might be the problem. The only thing I don't get is why it happens also on other laptops when I copy and paste the "IndexedDB" file into the new laptop.