Can you fire and overwatch while flying with Archangel armor?
A flying sniper CAN shoot/overwatch, but WITHOUT Damn Good Ground bonus.
Check this by press F1 key, before click OK button while shoot.
From XCOM Wiki "Flying DOES confer an elevated-position bonus, but you must fly higher than normal."
So fly higher please.
Sorry for my sloppy experience.
Yes, you can.
It's a common strategy to have a sniper with Squad Sight flying the whole mission on the edge of the map and kill everything, enjoying safety.