It actually changes the meaning of the sentence. "I have never realised" would mean that you haven't known that she has worked in a hospital until the moment you're saying that, in which you actually realise that. Saying that she HAS once worked in a hospital is actually incorrect, or better: it would mean that she has worked in a hospital just once, like.. A day or something. She WORKED, instead, means that she has worked there and that now she isn't doing that anymore. I hope I made myself clear :)

Yes and Yes. In the second sentence, I would remove the word "once" because it is redundant. By saying that she has worked at the hospital, you are already implying she worked at the hospital before.