If I have a vacancy, wifi trade with someone, and then set my 3DS clock ahead a month and go in as a new character and don't see a plot, am I fairly safe to assume I didn't pick up a voided villager? I just have to be super careful right now since I'm trying to keep a spot in which to move Freya.
If you don't see a plot, it's usually best to save with the new character if having no new villager is what you want, just in case. Can't be sure it won't pop up if you don't save it.
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If I lost the final minigame with a camping villager, will he ask me again to move here or do I have to quit without saving?
You can play as many mini games as you want. If you lose the move in game, you can try again until you win. No need to quit without saving.