So, this patient apologized to your patient for your patient having to be moved to another room as he was flu positive, and your patient stared at him and then ignored him. Yet, the patient with the flu was the rude one? It wasn't his fault that he was placed in a semi private room.
Yes, in my opinion it was wrong, and rude. Why not give him a bell and hang an unclean sign around his neck?
Yes, if all you said was that he needed to return to his room. What would have been better would have been to ask him to step away from the door while you were conducting shift report, and let him know that this was to protect everyone's confidentiality. You had already segregated him once, why should he be happy about this?
As the distance for which one could potentially be infected with an agent spread by droplet is approximately 4 feet, there really isn't much reason to keep the door closed.
Again, if he was standing in the door to his room, the chances of you, or any of your coworkers being infect were fairly slim.
It reads as if you were perturbed at him from the beginning, over something that wasn't his fault. While your patient wasn't obligated to accept the apology, you should have at least acknowledged it and let him know it wasn't his fault. Instead you, and it sound as if your coworkers did as well, ostracized him for the fact that he was there.
No, only if I'm entering a room of a patient with a known or suspected infectious condition.
Do you were a mask outside of the hospital during flu season? If not, why? You are much more likely to be exposed to someone with an infectious condition outside of the hospital, than from one of your patients.