HELP!! AWS vs GWS vs TWS

thanks again for your support. AWA is present (bottom part of the image, sorry not the best image quality) and looks good. Attached you find the requested log. thanks

The problem from your log is clear:
Your system sends a very bad MWD message, with TWA/TWD empty and TWS set at the same value as AWS received in MWV message.
I would either investigate why your system sends a faulty MWD message or filter out MWD message in NMEA settings in order to let qtVlm do the normal calculations in that case.

Maybe i need to change this setting (see image attached) so that the SW uses the GPS data to calculate GWS/GWA instead of STW to calculate TWS/TWA? The manual is not very crear about that 

No this is not related. According to the NMEA specification MWD should contain GWS/GWD but in practice this is almost never the case and it contains TWS/TWD.
Your problem is that your MWD is broken. It contains only TWS and it should also contain TWD or TWA, plus the TWS it sends is wrong:
$TIMWD,,T,,M,10.34,N,5.32,M*6B

But as long as the SW uses the boat speed (the stuck log) to calculate the true wind values of course the values are broken. I need the SW to use the GPS speed to calculate ground wind ones. Sure that that button does not do exactly this? If not, what is it for? Thank you for your patience:)

As I said it is completely unrelated to your problem. Your problem is that your receive bad MWD message, whether it is supposed to contain GW or TW data is another story.
Because qtVlm "thinks" it has a correct TWS in MWD message it does not recalculate it and uses what is given.
Filter out MWD message in NMEA settings and qVlm will calculate TWS/TWD/TWA based on COG/SOG, which is of course a fallback when no HDG/STW is known.