Is there any kind of list listing all the game prize items and where you can earn them from? And do game prize items come from just the games, how are they earned?

Well, Game Prize rarity items come from a lot of different places. Some do come from games, like comes from Random. Special quest prizes are marked with the Game Prize rarity though, as well as the plot prizes from Masquerade in 2013. Here is a list of all the Game Prize rarity items, you can click on them to find out where they come from but there happen to be a ton of items with that rarity, some of which aren't currently available, unfortunately.

Thank you once again! :D