Yes I have an update now.
I've got the car back yesterday after 2 weeks (!!) at the dealer.
They exchanged the fuel pump and the relay belonging to the fuel pump.
However this did not solve the problem.
After a long search, they found out, that the relay of the fuel pump is next to another relay.
And although the exchanged the relay for the fuel pump (according to the dealer documentation from BMW and even a BMW instruction movie for the mechanics), it turned out that the relay next to the supposed fuel pump relay, was the actual fuel pump relay.
So the position of the fuel pump relay was wrong in the official BMW workshop documentation and in the BMW-instruction movie for the mechanics!!
So this could very well be the reason that similar problems in oter i3-REX BMW's could not be solved.