Cayuga are wonderful! They tend to be quiet and very friendly. They can't fly, and can be dual purpose. Cayuga are my favorite. And they are gorgeous when they get their plumage! You can find more cayuga info at metzerfarms.com as well as many other breeds!
x2. You need to do something with the roosters. Rotating them will just make their lives miserable. Maybe set up a thread in your local forum? Someone might be willing to take a roo.
I agree with Deryk here. You will need to be careful if you do decide to move, your hen may abandon the nest. It is certainly up to you though! You know your chickens best.
Hm. Definitely, put some styptic powder on it to help stop any bleeding still occurring. I would put some disinfectant on it as well. Your rabbit should be fine though. One of mine lost a whole toenail once, and she is fine! As long there is no bleeding/infection she should be fine.