If I have 10 villagers and someone has a dreamy of mine, if I go talk to them is it possible for them to move in after one of my villagers moves out? I'm just still a big confused by this whole villager trading/cycling thing
If you have 10 villagers (even one in boxes ready to leave or even picked up with just a house that says moved out) you can not invite anyone to move in.
You must have 9 or less, this also applies to the campsite.
Usually villagers from other towns do not move in unless
A: You have less than 10 villagers and you go to the town of a villager that's recently moved out (like 1 or 2 days ago); you have a chance of getting him via Steetpass. I don't know whether the villager has to have been voided or not but I'm assuming they do.
B: You have less than 10 villagers and you go to the town of a villager who's in boxes; you can invite them into your town.
My answer would therefore be no, but about the first option: I don't know if it matters when you go into a town before or after a villager decides to move out. I myself don't know enough about this, but I'm sure others do.