Should I “intern” for a current undergraduate?

Answered

First of all, I would contact Harvard College and ask them if it is common and acceptable for Harvard undergraduates to hire high school or other college students to do internships which sound like grunt work to me.

Second of all, since it does sound very fishy, I would keep this person's name and contact information on file just in case they are violating any code of conduct. In the past I've heard of wealthy entitled students hiring for money, other students to sit in class for them to take notes, or in extreme cases, body double for them unbeknownst to the professors. Since everything is on zoom calls, this seems easier to pull off these days. Also, keep in mind that both at MIT and Harvard, since much of their undergrad curriculum is available on HarvardX or MITX and other MOOC open courseware, what many lecturers are doing in making their students watch canned videos that were filmed some years ago.

Seriously I would err on the side of caution here, especially if you want to apply to Harvard in the future. This will not look good for you if you put this on your resume and find out that this sort of activity is unethical and a scam. If it sounds too good to be true, it's usually a scam.