What is the ruling on KFC, and is what the father does—obtaining it for free or half price in exchange for his medical services—considered bribery and unlawful, and what is the ruling on the family eating from it?

Eating from fast-food restaurants is permissible as long as it is not highly probable that they do not adhere to Islamic slaughtering regulations or that they use pork fat. As for the actions of the restaurant workers in providing food to your father for free or at a reduced price, this is not permissible, because it is either an unlawful bribe or gifts to workers that are not permissible except with the permission of the owner. If it is without the knowledge of the establishment owners, then it is a breach of trust. Therefore, you must advise your father gently and kindly, and it is not permissible for you to eat from this food.