2. Why Is There Still Food? - Food Irradiation
So you can wander around the irradiated wasteland of post-apocalyptic society and simply pick up food like it's a frigging farmers' market? What, we're supposed to just accept that it's still recognisable, let alone edible, after lying around an abandoned hellscape for over 200 years?
Well, it's a long shot, but there could well be some real science in this that would make it all work.
Whilst it's true that most processed American food would probably survive a nuclear holocaust, but the following centuries might well see it decomposing into a mush - that is, if it weren't for all that lovely radiation.
Ionising radiation, as you may well be aware, is not super-great for living organisms, and this includes the bacteria and fungi that might cause your food to rot. If the irradiated landscape was sufficiently deadly enough, perhaps the land was rendered so sterile that the food simple stayed in suspended animation because there was nothing here to eat it.
We already know this works, because we're already doing it. One method used for food preservation is exactly that: Exposing it to radiation until all the bugs are dead.
Don't worry, you can safely eat irradiated food without sprouting limbs from your abdomen. Just steer clear of nuka cola.