Are villagers who are asked to leave the island able to come back?
Solution 1:
I asked a villager to leave and on my second mystery island I ran into them. So yes, it can happen. Not sure what the odds are, but I was honestly blown away.
Solution 2:
Yes, the villager can be invited back. Not sure on the Mystery Island encounter part, as I've only seen this done through Amiibo re-invites.