What's the difference between elköltözik and kiköltözik?
From what I know for now, one can vhova beköltözik - move in somewhere; vhonnan kiköltözik - move out from somewhere; and, perhaps, vhonnan vhova átköltözik - move from one place to another?
Wiktionary says it can take le-, fel- (when you move below or above sth/sb, I guess?), vissza- (when you move back somewhere?), and even szét- (I have no idea about this one).
The answers to your questions would also interest me.
I assume szét- might only work with anything plural (we you they):
Szétköltözünk. - We move apart (from each other).
I assume el means you move to somewhere. Away from somewhere / out of a place. Important is that you definitely move. Possibly abroad. Far away. Or to some space specified.
While ki means that you move out of a specific place. I think it might have a more local meaning. You might still stay in the same city. Important is that you move out and to where is secondary.