I tested your suggestion, but it didn't work. Then I decided to play with boot options and voilà! I got it.
At first I was using a legacy boot and then I changed to UEFI Boot.
Now I can start my note with the HDMI cable plugged and the screen will not be cropped.
The only inconvenience in this way is I must to press the boot botom, which is too small, everytime I want to play. But no worries...
By the way, I managed to fix that Mame Issue about not saving the settings. It seems this version 5.6 is missing some files comparing to the previous one. I had in my PC the 5.5 version and then I replaced and add the files related to Mame Emulator. I don't know where was thw problem, but it worked. Maybe you should use the files from 5.5 version in the next update.