I published a paper that received a bit of attention several years ago. A few months ago, I received an email from a student who expressed interest in my work. I don't know her, she is not in the same institution as I am, and she appears to not be located in the same country. I thought I was corresponding with a peer.
Later, I found out she is an undergraduate student who is doing her own research project with my model. She has been sending me emails asking very elementary stuff which she should have figured out herself and sometimes she tries to urge me to reply by implying what I did in my paper was wrong.
I answered a few of her emails just to clarify that what I did in the paper is correct. Moreover, from time to time, she said that she has severe depression and the deadlines were close.
What is the professional and ethical way to deal with this student? I don't want to waste time on this student, to whom I have no obligation to train, but I also don't want to increase her depression.
Currently, I plan to stop answering her emails.
Edit 1: After reading @Buffy's answer, I realized I forgot to mention an important point. At first, I thought the student was somewhat experienced in the field. After a while, I found out she did not know various basic concepts in the filed, so I pointed her to various introductory materials. However, the next time she asked a bunch of elementary questions that were covered by the introductory materials, as if she had never read the materials. Several days ago, she said she just wanted to finish thesis on time, suggesting she would just throw all things away after her thesis was finished. I felt very discouraged at the moment. At first, I thought I was communicating with a potential collaborator. After a while, I thought I could inspire a curious mind. Now I found out that she have never been interested in the things I discussed with her.