Question: Obviously, the guys don't believe that Bill has a son named Trey. Hank points out that the name was Travis last week. But why is Bill pretending to have a son?
Question: Why is John Redcorn surprised that Hank is not Jewish?
Answer: I don't think we can be totally sure, because John Redcorn has never, to my knowledge, said anything else about thinking the Hills are Jewish. This might be related to the stereotype that Jewish people are very careful with money. Hank and Peggy are known to be responsible and diligent. They don't make extravagant purchases, rarely do spontaneous things, and they maintain a comfortable and modest home. It's still a stretch to assume they are Jewish, but it's my best guess.
This also might be a mistake. In the episode "Revenge of the Lutefisk," John Redcorn was at the Hills' church, sitting with Dale and Nancy. He should know they are not Jewish.
Answer: Bill lives in a state of denial. He hopes his wife will return any day. He escapes into elaborate fantasies, like having a son.
Captain Defenestrator
I've noticed that Bill often wants to copy what the other guys are doing, as part of his fantasies. So if Hank and Dale are talking about issues with their sons, he wants to talk about a son, too.