Firstly - I don't think the book should be classed as Science Fiction (not in the truest sense of the genre).
Secondly - I found this to be an excellent book; the story isn't anything to do with "the end of the world", and the author correctly avoids any mention of whatever catastrophe befell the world. Although, in saying that, it is fairly clear that some kind of Nuclear War has taken place - the man's illness, the ash everywhere, the dead fish washed up along the beach.
The story, to me, was about the relationship between the man and boy - how neither of them were correct all the time (indeed, the boy was rightly scared when going down into the basement), how they developed over the course of the story (the boy more than the man) and how they learned from each other. It was maybe also about how people can survive - either through doing things they wouldn't consider beforehand (cannibalism, robbery, murder) or luck (fate?) in the case of the boy.
"What exactly is that hunting guy supposed to have survived on?" - I would suggest his caravan (his wife and children) had a reasonable amount of supplies and/or had the ability to find food as the man and boy did. It was somewhat suggested that he had come from an enclave or similar, so maybe they set out to find other "good" people. Explicitly stating how the "hunter" had survived wasn't really necessary - he survived as everyone else did.
