The employee is wrong. It works the same as with an apprentice.
An apprentice should either have it in their contract or have a signed a learning agreement which makes it clear either way. Especially a graduate apprentice who will be expected to do independent study.
You allow her the time to go to university when that is on. If there is no course on, she should be at work.
Depends on what they've agreed. If they've agreed she's at work when not actually in college, that's what should happen. If they've agreed she gets independent study time when college is closed, then that's what she gets. If they haven't said anything either way, then they need to sort something out.
perk
OP, When you stop thinking of studying as a "perk", and start thinking of it as part of your employee's working life, you will find it a lot easier to be clear about your expectations about where she is and when.
You have said that there are days when people take a long lunchbreak and other days when "something will kick off and no one’s feet touch the ground, you don’t even have a chance to look at your to do list until 4pm," I am guessing that what you really mean is that people don't just work hard, they stay late and miss lunch and work longer hours than they're paid for that day and they don't get paid overtime. So giving them a long lunch break is not doing them a favour or giving them a perk in return for working hard during the day. You are just using an informal way to make up for the extra hours worked.
You have a fantasy going on in your head about how your company is managed.