Solved! Go to Solution.
Problem solved: I received a testaccount from the spotify support. After logging in with this testaccount, it was clear that the described happenings have nothing to do with my iPhone/Windows PC. Everything worked will with the test account - syncing, deleteing, offline/online mode, playlists etc.
Therefore I decided to delete all playlists on my personal account. After deleting all, I was able to log in with my own account without any problems. I created the playlist, which was synced offline with the iPhone client, completely new, added all songs once again in 10-song packages, synced the packages - and it worked well. After syncing 14 10-song packages whily switching from offline to online mode, the complete playlist was "restored".
Now, everything works well. I can add, delete, sync and play like I did before! It was hard to rebuild the playlist, but now I'm happy 🙂