my issue is resolved. It was a hardware problem. The defect part was not the DAC+ Board, but the Raspberry Board itself. My guess is it was a problem in GPIO. With a replacement raspberry board it worked immediately.
thanks a lot for your detailled answer. In the meantime I did further testing. (New image etc.)
Also tried to deactivate the internal soundcard, and to enable digital volume control.
Nothing did help.
So my guess is: The Hifiberry DAC is broken.
I sent it back today morning, and ordered a new device.
Hopefully this will work…. If not I will be back with this issue on the board.