So here are the final results.
Black is black and white is white 
I am really happy now. In real life the white is a little bit more white than in the pictures. The light in my room is not perfect to make the white as it is in reality.
And to be honest: Black and White filaments got swapped by the printer a lot of times. Very very often and still no black shades in the white anymore
Summary: Updated values for the flush settings (max = 800 for the transition from black to white) and Prime Tower helped in my case to solve the soluation.