It depends on the situation you are in. If you are having a discussion with the person then no, it's not rude to ask what they do for a living and you can let them know what your occupation is as well. It's just curiosity and perhaps by getting answers from each other you may use each other's services in the future.
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.
If they want you to know, they would tell you.
No
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.
Masseuse.