She maybe didn’t want to ask you about your summer plans in case you aren’t comfortable answering. If you want to share, you could.

It’s ok for people to do casual chitchat. It would be inappropriate for her to share her problems (except maybe in context). It doesn’t mean you can’t share your problems in regards to job/training. It doesn’t suppose to be reciprocal. When I go to doctors etc I tell them my problems, I don’t expect or want for them to share their aches and pains. It would be kind of insane. I don’t care to know.

The fact that she doesn’t talk about her problems is irrelevant. You are her client, not the other way around.

She probably can’t help with health issues. I’d see a doctor about those. But you can share health issues in relation to job search like you feel anxious and scared of work with people or something (just an example).