How much of the food cost (and everything else) is tied to the increase in diesel prices? Do they adjust that out?

Distributor fuel costs are a really small part of the food price, with the notable exception of things that are bulky and full of air like Cheerios. The overwhelming fuel component of grocery consumption, by a margin so large you can consider it to be 100%, is the consumer's fuel. Driving 5 miles to an American grocery store to buy a few pounds of food is the most absurd scheme ever hatched. Having your groceries delivered by a van on a route is much more efficient but, perversely, by internalizing the last mile fuel cost that would show up as higher prices for food in aggregate inflation statistics.