1. The crew attending to the nursery, which includes Dr. Norman and various other vet students should be able to provide proper care to the downed cow.
I meant more long term, but let's run with this. Yes, they were vets and vet students. Does that mean they're prepared to properly transport a bleeding, flailing, panicked wounded piece of hamburger? Sure, you tranq her. Now what. You have a lift? You all going to drag her by a leg? Don't think so. You're not going to do anything about that leg out in the fairgrounds-- get Bessie to surgery! Right. The only care they really can and SHOULD provide at this moment is a humane euthanasia.
2. in order to answer #2, we have to ask whether the cow was euthanized, or kept alive. If it were euthanized, well, then that's it. However, if it were kept alive, we could place it in a sling, and additional care would be required to try to rehabilitate the cow after healing is underway. (possibly introduce practice of hydrotheraphy? even though very unprofitable to farmer)
So now the farmer is paying? The farmer is NOT going to pay to float the cow, because it should be dead at this point. Putting it in a sling has a lot of issues of the cow being down, and you can't just throw her in the Aqua Cow forever, because even if you float her, she's probably having issues with the leg still. Like mentioned by WhtsTheFrequency and others, THIS ISN'T EVEN POSSIBLE. I have seen people try as hard as they can to save a horse with a broken leg--- they all end up suffering and being euthanized. Barbaro, anyone? This just isn't feasible.
3. Dr. Norman is more than qualified to deliver the calf from the cow. Seeing as that is the main reason why pregnant animals are brought to the fair - for the public birth its offspring. Since this cow was brought to the fair...it had to be going in to labor very soon. The doctor and staff has all of the equipment to properly deliver, so why wouldn't they be able to do? as long as it is properly aligned in birth canal.
The cow probably needs surgery. How're you going to deal with the anesthesia and the calf, and she's very difficult to transport at this point. She's actually probably still rampaging around the fairgrounds with the bullet hole in her hock because that wouldn't actually immobilize her. Sure, maybe you can get the calf out fine. Maybe.
4. this is a question that is answerable only in proper context. No veterinarian WANTS to hurt an animal, but WOULD you injure an animal to try to save the life of the animal and the offspring? For some reason I can't get this question off of my mind. If nobody wanted to hurt this cow, then why was it shot several times by officers before finally passing? Public safety, i know. (Obviously it would take several shots for the cow to lose enough blood to where the officers and staff could intervene safely.) this seems like a slow death to me.
Yeah, context is really important. In this situation, the context would make it inhumane to shoot the cow in the legs, because:
1) no one would want to pay for the aftercare
2) the aftercare would be impossible
3) the cow doesn't have a chance
It's not okay to shoot the cow in this situation, and I can't think of a situation where it's best to injure an animal for human safety. Mother Nature gave us all that psycho adrenaline rush in dangerous situations to make us run on our pinky toes if we have to. Most animals will do the same, and injury isn't the magical solution you're suggesting.
They shot the cow several times because it was running, they were nervous, they were inexperienced, and it's hard to hit a cow when it's running FOR IT'S LIFE. I'm sure everyone would have preferred a clean shot to the head, but this isn't the perfect life you've dreamed up.
And 3-legged cows are usually called hamburger.