I think it's no contest which is smarter between a rat and a mouse as you may be seeing, though both make great pets.
The interesting thing about so called feeder rats is that the only difference between rats sold as feeders and rats sold as pets are that the rats sold as pets just happen to have more interesting coloration. They are often from the same litter. So feeder rats can make just as good pets as pet rats. You just happened to have 'lucked' out on a discount. Which may or may not be luck depending on if the feeder rat is already pregnant or sick from the careless treatment and abuse they receive from the pet store.
I'll answer some other questions for you too. As to whether they are male or female--which I'd figure out quickly otherwise you may risk a population explosion if any females you have aren't already pregnant due to careless mixing of genders by the pet store owners--while male rats may be able to retract their testicles in times of stress or fear, you can still sex them. If they are babies, their testicles may not have dropped yet, but once they drop at about 4- 5 weeks, there's no mistaking a pair of rat goulies once you see them. Here's guides to sexing your rats:
Be aware that juvenile rats can become pregnant at about 6 weeks of age. Females come into season every 3-6 days, rats mate in 1 second (literally), and gestation is as little as 21 days. She can deliver as many as 14 babies, and will mate again immediately upon delivery of the babies if a male is present and be pregnant /again/ while raising her current litter. These babies can breed at 5 weeks as well etc etc. You see how important it will be to figure it out as quickly as possible. Also, if you currently have females there's a good chance they might already be pregnant because the pet store will not take responsibility for separating sexes, so watch them carefully. If they deliver, we can offer advice on care and finding homes for the babies.
To answer your first question, rats are very social in nature. Like most social animals, they like to play and to tussle to figure out who's the boss of the cage. The pinning and grooming is normal behavior. As long as there is no blood, let them sort things out on their own. The pulling it to a nest may be a hormonal nesting behavior. The bigger one may be pregnant, or may have been separated from her babies (probable in a feeder tank) and still swimming in 'care' hormones. I seem to recall another question like this involving misplaced mothering instincts and how to deal with it, but I for the life of me can't remember what was said. Someone else here may have better advice on that. Here's a guide to interpreting rat behavior, which may prove to be a more interesting social experiment for your class: http://www.ratbehavior.org/
Once you have 10 (or was it 20? I can't remember) posts, you'll be able to post pictures and we can have a look at your rats to help you determine age and gender.
The smaller rat's sneezing is troublesome. Often because rats use their noses to explore their surroundings, putting them in new surroundings will prompt them to explore like crazy. They literally sniff more than usual, which means they get more stuff in their little noses, and they may sneeze more. This is known as 'new home sneezes'. It will subside after a couple of days. If your rat has been sneezing more than that, chances are s/he has contracted an upper respiratory infection, which won't clear on its own and will eventually get into it's lungs as full blown pneumonia. Time is important in treating this easily, so if you can locate a vet who specializes in exotics and/or specifically knows rats, then they can send you home with some antibiotics to treat your little bit before it gets too sick. Since it sounds like cost is going to be a factor in whether you are willing or able to care for them, shop around for a vet and be willing to explain your situation to them and that you have limited funds to see if they are willing to work with you. Some may be willing to work with you on only charging for the cost of the antibiotics, which as small as your rat is, may not cost more than $30 dollars. I purchased a digital kitchen scale from the store and am able to weigh my own rats in grams to call in to the vet to avoid the price of an office visit. You can get a scale cheaply for $20 dollars.
Proper pet care is never as cheap as actually buying the pet no matter what the pet. Though if you are willing to spend time with your rats, you will find that they bond with you and become just as rewarding as dogs or cats in terms of train-ability and affection.
Good luck with you, and I hope you end up choosing to keep and care for them properly as pets. They'll be rewarding and very enjoyable additions to your home. If not, please consider looking to rehome them with someone who will care for them rather than send them back as snake food. Best of luck to you!
And as I said, if you need any advice in figuring out how to care for your rats, from housing onward, we'll be happy to help.