"Teşekkürler, güle güle!"
Güle güle is said to someone leaving BY THE PERSON STAYING. It means "smilingly/laughingly/happily" and is short for "Güle güle gidin" -- so it's like saying "Go forth from here happily!"
Hoşça kal(ın) is maybe slightly more often said by the person who leaves (not a hard rule, though--can be said on the phone, or when two people part, or even by the person staying). It means "Stay nicely/well."
So if a couple of friends go to a cinema and after the movie they go home, then nobody would stay güle güle, right?
Generally not. Unless, you know, one person is dropping the other person off and is in some sense "staying behind" the other one. I could picture saying it to someone getting out of my car, or maybe if I walked them to the metro to see them off (but it's a little weird and nonstandard).
Yeah, but it's still limited in usage as described above. Most definitely ONLY said by someone staying behind to someone leaving. Since we don't have that context in English you're stuck trying to pair it up with generic ways of saying goodbye.:)
Güle güle was the only word before Duolingo I knew about turkish