I am going to only address the later..... That is what I was wondering. If the defect remains as just physical or if it mutates the gene as the chick is developing.
It depends. While the genes of the chick are inherited (assuming with no defects), it is indeed possible for a mutation to occur during development. So there is a clear delineation between a chicken with a physical incapacity, and a genetically malformed chicken. The first, like a chicken with a twisted foot, should not be transmissible. But the second, such as eyes or feathers without pigment, or deaf, could potentially be transmissible. That's how genetic sports are made, and throughout history they have created both monsters (sorry, Chinese Crested Dog) and wonders (most of our heritage flowers and fruits).
Without the ability to analyze DNA, the only way to find out is to breed many offspring and see if any carry the defect, or if their children do if bred back to the defective parent.