infered5

All you can do with Steam when it comes to game sharing is the Family Sharing plan, which is very restrictive. When you both enable Family Sharing (Steam Family Sharing Article), your libraries are "shared" and only accessible to one person at a time. If you share your 1000 games with your friend who has 5 games, you can each only play any of the 1005 games when the other is not playing. It's so there aren't large accounts with many games that people can buy access to.
 
TL;DR you cannot move steam game keys.

It could be your GPU acting funky, swap it out for one of your girlfriend's R7 360 and see if the same artifacting happens. If so, try to RMA the card under the warranty.

I use Family Sharing because my brother doesn't have a PC and I do. Since we live together, we're the perfect choice for Family Sharing. If you have a friend with his/her own PC and library and you play together, it is NOT recommended to use Family Sharing.

Technically you do not own the games you bought on steam but rather have a "subscription", as for sharing games it is possible using the sharing method as many others have said but the two of you would not be able to play that same game together.

This is the only thing I can think of off the top of my head.