I think all of those questions are important. Further, I would ask how often they breed their females. Ask if you can come visit and observe the dogs' living conditions for yourself. Ask about the parents' parentage. How do they bring up their pups? Do they start them on housetraining? Are they socialized with lots of different kinds of animals and people? How do they do it? What do they send the pup home with? How do they do pet delivery? At what age do they send the dogs to their new homes?
Any one of the answers to these questions could raise red flags.
