Does tunning a channel on the VCR show color? If b/w picture is only
from tape it could be the heads have clogged or the recording is weak.
Try another tape or try to make a recording and play it back. The
chroma signal is recorded separately on the tape as a low frequency AM
signal.

When the aerial cable is disconnected and the VCR and TV are connected with
coax, the VCR menus shows fine on TV, with blue background. As soon as I
connect also the aerial cable to the VCR, the screen gets b/w and shows a
lot of disturbances ("snowstorm").

Then I removed the coax cable between VCR and TV, connected them with SCART,
connected the aerial cable to VCR, and switched TV to external input. Now I
can tune channels in VCR, and the channels show with colors on TV screen.
There is however some disturbance in the pictu flickering, fluctuating
grayish horizontal lines. This does not exist when receiving the same
channel with TV receiver. Starting to play a cassette makes the picture b/w.
Another cassette makes no difference.