stretching a resolution that the game was not designed to run at, the graphics will be pixelated and I think QHD is something that stretches it while not pixelating the graphics.
if the game doesn't offer higher resolutions the monitor won't run them. As far as I know you can't run a game at a higher res than it was designed for.
I expect your game playing experience won't change. If you play at 1080p it shouldn't have black screens.
QHD has more pixels to throw around so it just makes pictures more detailed in most cases. in some games it will give you more picture, it depends how game is coded , but it shouldn't stretch the pictures. In an old game I have, it doesn't add more detail to the characters, it just means you can...