Does anybody know a way to permanently assign application to specific activities?
I like to say: this app should map to activity1 and activity2, but not to 3 or 4. This should be remembered upon system restart. When I start this application in activity 3, it should also be linked to activity1 and 2.

Is this possible, and if yes, does anybody know how?

The best you can do for now involves using sessions.

1. Set your system to either load a manually saved session or the last used session (System Settings -> Startup and shutdown)
2. Add your applications to the activity
3. Stop the activity using the activity controller
4. Save your session (if using manual save)

At reboot, restart the stopped activity.