.. the deployment card is returned to the imperial player's hand so that an investment of threat points will get it back into play?

Or is this just true for open groups?

All groups that are not unique. See Defeated in the RRG. Also see Deployment in the RRG.

So in the first mission, when rebels killed all imperials outside the door,

I would be able to bring the Stormtroopers back to game at the start of round 4, by paying 6 threat?

No. You deploy/reinforce during the status phase not at the start of the round. But, yes, during the status phase, you could spend 6 threat to redeploy the stormtroopers.