Pokemon Zeta / Omicron

These games would be great but they feel so out of place when they aren't on my 3ds

Also how do you save this thing? Like wheres the save file?

By saving in-game. There isn't save states like emulators such as Desume have. But I believe you can run multiple games at once (there is a Save File option on the start menu, so you can play up to 3 games without deleting data.)
I think the save file is the Game.rxdata file, which is C:\Users\Owner\Saved Games for me.