It sounds weird, yes. I TT'd her out on accident not realizing I was in a moving cycle. She is now in my kids' town and not original at all.... So I would like to trade for another Diana If the not original part is a bummer for you, I can pay damages!
Yeah, if a villager leaves, no matter what - you have to go through the fun task of cycling out 16 other villagers in order to get that one back It's a sucky rule.
No, only move outs count! The only way to know is to either try to back track (checking move out letters or just remembering) or if you think you have cycled through then you could always find someone who has her in boxes and try to ask her to move in, she will give you the option to move her in if you have cycled enough.
You could also use the tree in your plaza to see your town's history of villagers, right? I'm pretty sure the credits there say who has lived in your town in the past
Yup, the tree only shows current villagers, but here's the good news: The villagers that have moved out of your town will appear on mainstreet, after some time Diana will eventually appear on your main street (where the shops are). She will no longer appear once your 16 villager cycle is complete, that's a good way to know for sure.