Is it legal for a minor to be hired by a college to take notes for students with accessibility difficulties?

YMMV based on location.

What you would be doing by selling your notes is the equivalent of selling a good or product you produced yourself. Since it's not working for a wage, you should have no legal issue doing this, though there may be tax implications if you are claimed as a dependent by anyone else.

The agreement to purchase also presents an issue, as minors under a certain age cannot enter into a contractual agreement on their own.

It's also important (and a given) that you don't misrepresent yourself on government forms such as the W-9. That being said, the W-9 should be the least contentious part of this whole arrangement.

If I were in your shoes, I'd go for it even if I couldn't legally enter a contract. Typically the legality of your signature on a contract only comes up when the contract comes under contention (failure to pay/failure to produce/etc.).

In most states, you can get a paying job at age 16^*, so yes, it's perfectly legal to sell your notes.

^* Heck, I had a paying summer job at age 14 (but that was back when only bike racers wore helmets, and kids rode in the backs of pickup trucks).

This sounds like a fairly standard arrangement, often used when there's a student in the class with a disability. For example, here's one college's Peer Notetaker page: https://www.lincoln.edu/peer-notetaker-ssd

The college should be familiar with any legal issues related to hiring a minor, but if it's a W-9, I don't think there would be any. A W-9 means you'll officially be self-employed, so any child labor laws probably don't apply*. Note that you'll probably receive a 1099-NEC and need to pay self employment tax at the end of the year.

Being under 18 may mean the contract isn't enforceable, but I doubt the college would see that as in issue, since they can just not pay you if you don't hold up your end of the contract.

_{* I'm not a lawyer, so consult a lawyer if you need a legal opinion.}

There's a difference between void and voidable, and a contract with a minor is the latter, not the former. There's little case where it being voidable would be relevant; if you are paid before delivering the notes, and don't deliver the notes, the university still has a claim against you; if you void the contract, you need to return the money gained from it. If you say that you'll give the notes, but don't (and aren't ever paid), you can void the contract to avoid a breach of contract claim, but even if you were not a minor, the university would be unlikely to pursue someone who flaked out like that.

And while the Agreement to Purchase is technically a contract, that's not really the main purpose. It's mostly a paperwork thing: they have documentation that they can show if anyone audits where their money went, and you and the university have a written statement of what each party expects (you: money, them: notes).

It's probably a good idea to speak with a parent, anyway.

As a minor, you are free to sign contracts, there is no legal problem for you. There are laws in place that are to protect you as a minor, so if there were any problems, they wouldn't be your problems, but someone else's.

Since you are a minor, you and your guardians, which are usually your parents, can void any contract that you signed, until a short time after you are 18 years old. If a contract is voided, it is legally as if it had never existed. So you then have no obligation to take these notes, and the university has no obligation to pay you. Only you and your guardians have that right. The university is bound by the contract unless you void it. And nobody has the right to modify the contract. So you can change your mind and void the contract, your guardians can decide against your wishes that they void the contract, but the university can do nothing. They are bound by the contract unless or until you void it.

If I, as an adult, sign a contract with a minor, I'll obviously keep in mind that you can void the contract. If that is too risky for me, then I'll have to find an adult. For example, I wouldn't sell you a brand new car because you can drive it for three months, and then void the contract, and return a used car without paying me - too risky. But if the contract says "You do the job, and I pay you", that's not a big risk. Worst thing that can happen to me as the adult is that you don't do the job, and I don't pay, and I have to find someone else.

Your university will have done the same thing and thought about the risk. It's a low risk to them, the worst that can happen to them is that they don't get any course notes and you don't get paid.