If you have a good reason for asking, it's probably not rude. "Old" person? over 80 is old to me and those folks are usually proud that they've made it that far and don't mind answering. Between 25 and 80 folks can get sensitive about it. That's probably because they don't like to think of themselves as "getting older", just "getting wiser". Don't go there unless you know the person well or have a very good reason for asking. most people say it is rude to ask someone older than you of their age, but i think otherwise. it wouldn't be rude at all if you asked him/her with respect...
it is personal.
No, it is not considered rude to ask someone their pronouns. In fact, it can be a respectful way to show that you value and respect their gender identity.
Yes
Asking someone for their pronouns is not considered rude; it shows respect for their gender identity.
It is not considered rude to ask someone how to pronounce their name. In fact, it shows respect and a willingness to learn and correctly address them.
Yes, that question is personal.
No
If they want you to know, they would tell you.
To stay away from someone that is rude in your class, you can ask to switch seats with another student.
Yes, of course you can. [although some ladies may think it rude to ask]
You don't need to ask why. Just be gracious and thank them.
You may ask twice before it is considered rude.