Do you earn money while shadowing a profession?

Generally not for just job shadowing, but some internships pay you if you actually do work instead of just observing (the key word there being 'some').

Do you mean after you had a nursing degree? I doubt it. I mean, when you're first hired at some jobs, you might have a mentor or something, but you would be paid because you were working there. I doubt they pay someone to shadow. If you shadow someone, you are observing and learning. Why should they pay you for that? It's not like you're helping them.

No you don't get paid for shadowing.