Hi! You have very interesting questions and I'm enjoying your enthusiasm. I'm also a college student (zoology) and got my first betta a few months ago. A word of caution: Don't let him distract you too much. I have to study in the library now because of my fish! (I brought him into my home and he kicked me out!)
On the Eye: There is something called Pop eye and depending on the cause, it can be helped. That's all I know about it. There are sites that cover it and there are books you can probably find in the library. Missouri? You have a vet school and I bet they have a library that will help.
You need a heater and a thermometer. Ambient temperature matters. Fish are ectothermic, so you have to find a way to apply heat. Lamps may help in a small tank. My dorm stays cold even in 50F weather (in the south, that's cold) Also, I suggest getting the biggest tank you can afford and the dorm allows. This is more because you will be too busy to give him the frequent water changes he needs in a smaller tank. The initial cost is kind of high (my 5 gallon tank was $36), not to mention all the accessories needed, but it's worth it if it means your new roommate is healthy and happy. Just make sure it's spacious and has plenty of air-water contact for maximum oxygen diffusion.
Watching fish is known to reduce blood pressure. I've also found my betta to be therapeutic.
Holes in his fins could be fin rot.
If you take pictures (really good ones that are well lit and display your concerns well) you can post them in the other blog about sick bettas and ask for opinions on what he has and how to treat it. It's great for getting quick responses when research would take days.
There is such thing as photophobia. A flashlight will help determine that, I THINK. (Swear by nothing I say and understand I know nothing)
Moving a betta can stress them especially if they are already compromised. If he is ill, you want to do as few water changes as possible while helping him (this is where bigger tanks are nice) and make those water changes as stress free as possible.
I understand your fears of leaving him at home. I have a bird that lives with my parents and I nearly cried at the site of her cage. I would never leave my fish with them. He would die and I'm surprised the bird has lasted this long.
Fish interaction: It happens. They are smart. They watch you and know when you're looking at them. Mine swims up to greet me. Do they ask for food? I think so. Mine "dances" where I put his food every morning around 8. Toys? There was a floating rock my fish messes with from time to time, but I think he is testing it for edibility. You can train them. Classical conditioning.
Plants: I have lucky bamboo in my tank. It's been there a week and we've had no problems. He was playing with a piece of root yesterday.
Have fun with your fish! He seems to be in good, caring hands. They ARE entertaining! They have their own personalities (much to my surprise) and I suspect that once you get him a permanent set up, he'll relax. I hope that helped. I've found looking stuff up and getting help from people here to be great. You'll gain your own knowledge as you go along- it's really fun and amazing.