Yes, I also switched the USB cable of the touch screen to either the RPi and the Mint box and I tested it if it worked (albeit not calibrated) before I ran the commands.

I must admit: I also find it strange why the "xinput calibrator" works just fine on the RPi, but it doesn't succeed in calibrating the same screen correctly in Mint...When I run it in Mint, the cursor remains in the 4 corners when in tap it in the area of the corner, but is not able to reach the rest of the screen...

So I guess this is it: the only option I have left is to cave in and buy a Windows licence. I would have preferred avoiding this, but I guess I have no other choice now. Oh well...

Thanks a lot for all your help!