Although Outwit doesnt use an action, can you not use it with someone you've already used in the same turn, or can you? Like if I move my Batman on top of a building, can I make him use Outwit on Mr. Fantastic's Invulnerability right after I move him, or do I have to wait until the next turn?

You can use it any time during your turn!

Just not in the middle of an action. But you can use it then move or move than use it.