"Microsoft".
It's annoying. It clearly detects the hotkey press but the drawing of the overlay seems to crash(can see it in event viewer). Considering they wrote directX you would have thought they'd be able to write their injection correctly to support fullscreen.
I used to have a similar issue with AMD relive.
I would still suggest leaving game mode off it seems to do more harm than good. From reading around it appears to emulate fullscreen from a borderless window. So you may get higher fps but you will get an increase in Input lag.
Haven't noticed any input lag, perhaps the input lag only applies to mouse and keyboard? I haven't gamed on a mouse and keyboard since League of Toddlers and aint played that since '06

Depends on the game, some games giver better FPS while others can give worse FPS in borderless. The biggest draw to borderless for me is the fact Bethesda games seem to crash everytime you try and ALT TAB from fullscreen which is a pain for someone who works from home.I have always used Fullscreen for all gaming, never seen the point in using windowed/borderless, any benifit ?