You’ve got a great chance to teach your summer student about the proper treatment of wildlife by doing right by this little rabbit.
The front leg issue: Not good. You’re right in that rabbits don’t usually get splay leg in the front, though it can happen. My guess is that it’s either from lack of a proper diet or living on the wrong kind of surfaces. Either way, it does need to see a vet or at very least a wildlife rehabber who can fix the issue.
The diet: Stop with the milk, please. Cottontails nurse for about three weeks, maybe four if mama really likes them. But basically once their eyes are open, they are ready to eat solid foods. If this rabbit had its eyes open when you found it, there is absolutely no reason you should be offering it milk anymore. Stop the vitamin supplement. This stuff is basically junk and by offering it you might be causing a massive vitamin imbalance which hey, can cause leg problems. The very first ingredient in the pellets you are feeding should be alfalfa hay and there should be no colorful cereal bits or seeds in them. Feeding alfalfa hay along with an alfalfa based pellet is going to be too much calcium and protein for a rabbit, even a young one. Stick with the timothy hay. And also? Stop the yogurt treats. It’s like having a Big Mac for a snack everyday.
You asked the reasons for not keeping wild animals, so here’s a great one: It is a well known phenomenon with cottontails that they tend to waste away in captivity. Some don’t, and that’s great, but most do. After a few months they may stop eating and drinking, they may start thrashing around in their cages (not running circles, but actually running into/climbing up the sides). Eventually they will dehydrate, starve, cause an intestinal compaction and die from that, or injure their necks or backs and die trying to escape. Most of the time, you just come home to a dead rabbit, though. I don’t think that’s going to thrill you or your student.
In addition rabbits, like all animals, occasionally need vet care. The leg problem should probably be seen by a vet, but rabbits are also prone to hairballs (They can’t vomit, and a severe hairball requires surgery or it usually results in death), upper respiratory infections, and broken limbs. It’s also a good idea though not a requirement to have a pet rabbit spayed or neutered. Are you or your student prepared to attend to this rabbit’s needs in those cases?
Assuming your cottontail lives, they have a lifespan similar to a domestic rabbit–6 to 10 years or so.
What it boils down to is that if this rabbit had its eyes open when you found it, it was ready to be on its own. You could have moved it to a safer area if it was in danger, but it would have been better left alone after that. There is no reason for it to be on milk now. It would in this rabbit’s best interest to be handed over to a wildlife rehabber who can hopefully fix its legs and let it go where it belongs. Not doing so could condemn the rabbit to a fairly pointless death. In a best case scenario, you (or SS) are stuck with this rabbit for the next decade or so.