Any service member of superior rank is due military courtesy such as saluting officers of superior rank. Any NCO or officer can make "on the spot" corrections like "your rank is on sideways" or "your boot is untied".
Command is a different matter. I was in the Army, but not any officer could give me an order even if they were Army. Only officers and NCO's in my chain of command could tell me to do anything. I was in a joint command meaning a Navy or Air Force guy could be in my COC but some Navy dude could not walk up to me out of nowhere and tell me to do XYZ without clearing it with my COC.
Correct. I also never wore rank or unit patches. If I did it was whatever suited the situation.