1. I agree with what Jade said and get a thorough check up of the chinchillas from the fur farms. If you can obtain pedigrees from the fur farms, that would be something good to have.
2. Do you know the background of the breeding pair? I think when it comes to breeding, knowing the backgrounds of all chinchillas is a very important aspect of breeding. Do you happen to know why the male died? Was it something that can be passed on to the offspring? If so, I would not breed the offspring.
3. If you are solely breeding for yourself and not selling the offspring, then yes, that is fine. Everyone breeds for a different purpose. Most people will agree when breeding a specific animal, it is to better the species so you have to think of what your long term goals are.
Quality is such a broad term and has various levels for some people. The traits that come to mind when thinking of a high quality chinchilla are blocky, has dense fur, healthy and preferably has the Brevi characteristics. If you are breeding just for yourself, then it isn't absolutely necessary to have a chinchilla that is blocky, dense fur and Brevi. The most imporant aspect for you is to have healthy chinchillas that do not have any genetic flaws.