Hello jan_bache,
Thanks for that info and for choosing the Apple Support Communities. If I understand correctly, you are unable to end a FaceTime call. At this point, we would like you to reinstall iOS on your device; this will help us isolate the situation further. Reinstalling iOS should not affect any of your data, but it is always a best practice to make sure you have a current backup in either iTunes or iCloud.
How to back up your iPhone, iPad, and iPod touch
Transfer photos and videos from your iPhone, iPad, or iPod touch
Once you have a current backup, follow the steps from the "If your device turns on but gets stuck during start up" section in this article:
If your iPhone, iPad, or iPod touch won't turn on or is frozen
Use the “Update” option and not “Restore” and these steps will reinstall iOS. Keep in mind that these steps were written for a different issue, but they will still help us isolate the situation further.
Cheers!