I have experienced something like this once in my career. However, the man was not my thesis advisor, nor a member of my graduate committee. It did not discourage me from pursuing a career in science. There have been some widely publicized cases of very influential scientists who are known for this sort of interaction with women students and young professionals. So I know that it does happen. On the other hand, I think this is relatively rare, though it is obviously very difficult to handle when it does happen.
I think the email mentioned at the beginning of the article is totally out of line, because the man writes that he has helped the woman’s career and also there is a comment later in the article that she needs his signature on her thesis.
My suggestion would be that the woman should talk with the department chairperson, or if she is not comfortable doing that, with someone in the Women’s Resource Center or equivalent, or with the Ombudsman, if the university has one.
As I read the article, it appeared to me that some of the other over-the-top personal references were in emails sent by other faculty members to other students. Assuming that these are separate emails from different people, then the rest of my advice follows:
At my university, something that is an expression of interest, but that is not overly personal, is actually allowed, if the faculty member does not have the student in a class and is not a member of the student’s thesis committee. In that case, an expression of interest that is not sexual, or even a couple of expressions of interest, does not in itself constitute harassment. In this case, a polite declination of interest is totally fine, and should shut the comments/emails down. If it does not, then continued expressions of interest do constitute sexual harassment.