Now my promised update:
Since saturday I am trying another Apple TV4k (from a friend of mine) with following software versions:
Apple TV4k: 11.2.1
Netflix: 1.15.1 (from 11 Dec. 2017)
All other setup was not changed. Same HDMI cable, same TV software (Sony Bravia 4k, Android TV 7.0, latest software - Europe Version from November 2017). The only thing I did was disabling WiFi from TV because I had problems by playing music via AirPlay.
Results: All problems are solved. Netflix shows video directly (no rebooting necessary). Switching framerate and contrast between different files works very smooth.
For me it seems that there could be a problem with the hardware (Apple TV4k) Tomorrow I will call Apple hotline to ask for changing my Apple TV into a new one...
One more thing: Netflix also shows „Dolby Vision“ for some shows again. But — for example Stranger Things 2 — Netflix shows on my iPad „Dolby Vision“, on Apple TV only „Ultra HD 4K“ without Dolby Vision. I do not know why...