You want to play word games? We're talking about novel understanding and you want to play word games. Ones that you copy pasted. Okay. I mean no offense but those ones haven't worked in a few months. All of this talk about how intelligence requires novelty and you copy paste. But here's the answers, I did not alter the prompts or allow it to search the internet:

The doctor is the boy's father.

This is a trick variant of the classic riddle. In the original, the father is in the crash, so "he is my son" seems impossible until you drop the assumption that surgeons are men — the answer being that the surgeon is his mother. Your version swaps the parent: the mother was driving and is in the waiting room, which means there's no puzzle left at all. The doctor is simply his dad (or, equally validly, his other mother in a two-mom family). The only trap is pattern-matching to the famous version and blurting out "the doctor is his mother" — which the setup explicitly rules out.

and

Drive — because the whole point of the trip is to get the car to the car wash. If you walk there, you arrive with nothing to wash; the car is still sitting at home.

The 100-meter distance is a red herring. For almost any other errand that short (buying milk, dropping off a letter), walking would be the obvious choice — faster than starting the car, healthier, no cold-start engine wear. But this errand's cargo is the vehicle itself, so the car has to make the trip. Drive it over, wash it, drive it back.

They've had trouble with forming dialectics before. I haven't tried with Fable yet. Maybe you could start there? IDK