Can you fire a rockets with an aa gun and move it in the same turn? (nt)

I would say so, just like a bmb moves during non combat after SBR, an AA can only move during non com, i see no reason it cant move after firing.

Especially considering the rules forbid it from moving during the combat phase

No.  Land units that have participated in combat may not move in noncombat movement.

What a scam! :s