Finally I solved it myself.
If anyone is facing kind of the same trouble as I did this might be a solution:
Silverstripe seems to get confused if you define the default language after creating some sites and then activating the translation.
So first all you have to do is delete all pages you created for your second language so that only your default mother language sites are left. Then go to the Database table 'SiteTree' and ensure that the field 'Locale' has everywhere not only a but also the same value, in my case 'de_DE'. Now you should be able to create foreign language pages without any weird UI / frontend effects.