score:5
I'd give Airbnb a shot, though I never tried it personally.
In Germany such short-term apartment rentals are indeed nearly impossible. However you can maybe find something called WG - a roommate arrangement. Some of them may accept a short-term rent, maybe to fill for a sport which would be otherwise empty. A popular website to search for such places is http://www.wg-gesucht.de/.
Upvote:0
If you are young, love company and can turn an eye to a thing or two, maybe you could give a shot to https://www.couchsurfing.com/ too. That maybe absolutely free anyway...