From what I know, although I've never tried it, if you haven't started up an existing character, you can TT back a day. I'm not 100% sure it'll work, though.
If they're already in boxes, there's nothing you can do.
Nope. Sometimes villagers will change their mind about moving and not actually be in boxes on the day they are supposed to, but ones they are in boxes they will move no matter what ):
If you haven't played in like a week I'd suggest ALWAYS starting up a new save to check for any movers before you load your major, it only takes a couple minutes and will save you a lot of sadness and time later on. I always do it and have never lost a villager on accident in years of playing since I got New Leaf on any 3 of my copies. Knock on wood. XD