Have you tried the website biroto.eu ? They have amalgamated a significant number of bike routes across Europe. The section covering Germany, and more specifically Berlin/Brandenburg (where I live) is really good. All routes can be seen on a map as well. They do not list sections that are 'car free' as such, but the routes I have followed have been pretty low on mileage alongside cars, sticking instead to rideable paths and trails.
Have you tried the website biroto.eu ? They have amalgamated a significant number of bike routes across Europe. The section covering Germany, and more specifically Berlin/Brandenburg (where I live) is really good. All routes can be seen on a map as well. They do not list sections that are 'car free' as such, but the routes I have followed have been pretty low on mileage alongside cars, sticking instead to rideable paths and trails.