Congrats on your new pets. I've owned two chinchillas so far and have enjoyed caring for them immensely.
I'm no expert but the white one looks a white mosaic. If its sibling is ebony it could be an ebony white. Perhaps someone else can comment. The mottling on the ears may indicate it is an older chinchilla.
Normally when a chinchilla experiences fright during a fight or when it gets startled in other ways the hair will easily slip out. It always grows back on its own and can take a few weeks but can take longer for an older chin. If you don't see new growth after a week or two there are likely other health issues involved.
The condition of its fur looks pretty bad and appears you have a fur chewer, especially on the tail, but I could be wrong. A fur chewer will mow down its fur usually to the undercoat when it gets bored and the chewing will be the worst on its back and tail. Fur chewing is not dangerous and some animals will do that throughout their lifetimes. Sometimes fur chewing can be caused by stress and may improve or stop when the stress is removed.
((((Your chinchillas should be kept in separate cages if they are not already. That kind of fighting you describe can easily lead to fatal wounds. I've seen photos of chins killed in fights and they are truly horrific. Also it causes stress that can lead to sickness and malnutrition by causing the subordinate chin to stop eating or drive it away from food. The first two weeks after relocating are usually going to be pretty hard on the chinchillas, especially the first few days. It is important you have them on a good diet and keep them in a calm environment. Withhold all treats until their droppings look normal.))) --See post below. I was assuming these chins were not bonded.
You don't want to introduce stress when they are associating a new environment or you could be setting a bad precedent. It's best to not let them out of their cages to handle them unless they act tame enough to come to you. Getting to that point can be a process depending on how tame the chins were when you got them.
I do have some questions for you. What diet are you feeding? What kind of treats have they been getting? What kind of cage setup do you have? How old are the chins and what are their genders? Does the white one chew the fur on its back and tail or its its fur just that short?
