The resolution of the game screws up (goes lower resolution) and for some reason my GPU started to run like crazy when i was on the desktop after alt+tab or pressing the windows key.

Yeah I have the same issue, it seems to only go back to my original resolution after I quit to desktop and relaunch the game. Have you discovered a fix yet, or do we just have to run the game in borderless window?

Edit: I changed the fallout 4 ini found in my steam apps folder to match my resolution, and the problem seems to happen less now.