Concerning the left window zero - it was not set in fact. At the original measurements there was the Left window zero without problems and it was left for averaging, too. (Usually I adapt the left window so that the correct phase response were achieved - a problem with the noise or so.) The matter of fact is that if the vector average is made, then the reference point (Window Ref Time) is automatically set to the peak sample of the resulting impulse response (0.038 ms in the examined case), and if the Left Window is set to zero, then the result is wrong, because a part of the impulse is lost for the frequency response calculation. If the Ref Time is set to zero manually, then all is O.K. even if the Left window is zero still.
Now it is all clear for me, but I think it would be better maybe if the Window Ref Time was not changed at the vector averaging. However there could exist another problem perhaps, what Ref Time should be used if these for different original responses were different. It seems at the existing state the first peak sample is chosen.