Probably not. It might be a pain in the ass but realistically you'll be able to work with banks/utilities/work to get access back. As long as you have access to your email as well you can likely recover your accounts. Files are likely the biggest risk, remember to keep regular backups and even this can be recovered.

It depends. If everything is stored unencrypted on the drive it's pretty easy to reset passwords or boot to a USB and access everything. If it's locked down hard you could be SOL. The worst I've seen happen is the loss of family photos with people who had passed away so they were irreplaceable.

Is it though? I definitely had teachers in middle/high school with oddball requirements like "only physical books more than 10 years old are valid sources". Total nonsense but it does happen. College is a place where you are meant to have these bad assumptions challenged and corrected. Presumably after a response they'll be better for it.

I don't think I'd use them for anything other than their intended purpose if you don't know exactly what's in them. For the leaky ones, you could probably collect the gel into some other sealed container like an old jar (not totally filled). Then it would still work well as a cold source for coolers/lunch packs.