Should I send a copy of a closed-access paper requested on academia.edu?
I'd send the article.

I am not a lawyer. However, it's quite common for people to send me e-mail messages requesting reprints of my papers. The Academia.edu and ResearchGate websites have mechanisms to request a reprint of closed-access papers for similar reasons.

Now I think it depends a bit on the journal. The chemistry (ACS) journals that I tend to publish in, allow 50 reprints in the first year, and unlimited reprints after that point. So far, I haven't run into trouble with exceeding 50 requests for a paper in the first year. I'm happy to e-mail PDF reprints or handle them - in my case through ResearchGate.

Your mileage may vary (i.e., depending on the journal). Personally, if the journal expressly forbids sending such reprints, I'd find a different journal for my work.

In my opinion, blocking such infrequent requests for reprints impedes scholarly work.