Is it rude to yawn immediately after someone begins talking to you?

Yes, it is rude if with mouth opens and sighing. Since yawning is controllable even you are tired, either you can yawn with your mouth close, or a hand over your mouth to show you are not doing it on purpose or with intent that you are bored. *

It depends on the situation and the person. If the person are close to me, like a friend or a family, I wouldn't mind. But if it is a person I hardly know and I am trying to discuss an important matter, then I would find it rude.

It is, but don't judge them for it. Yawning is involuntary.

Depends what type of person they are. I personally wouldnt mind, I would just see it you being tired.

Yes, but apologize immediately and it should not be a problem.

Yes but I am always tired so it is what it is

In Japan it is..