Was he left mostly to his own devices without much human interference when he was a barn cat? This sounds like the behavior of an animal that knows it's not on the top of the food chain and hasn't been raised in an environment that shelters him from that reality. It's a tactic to disguise his scent and his presence from other predators, and like catloverami said, they will often bury their food to hide it from other animals when they can't finish it all in one sitting.
As for the food issue, I'm guessing you free-feed? That's not really necessary, as cats are built to hunt and gorge, not graze all day. The design of their digestive system actually does better with periods of no food between feedings. For a domesticated cat, it's safe to go up to maybe 18 hours or so but they will probably let let you know they're kind of hungry every 4 to 8 hours, depending on how big their last meal was. Put the food down and what he doesn't eat in 30 minutes, take it away and put it back later when he's letting you know he's really hungry.
Sorry, I don't know what to do about the litterbox thing. Do they make weighted ones? If there is such a thing, that might at least help with him not being able to drag it, though it doesn't address his feeling of needing to. But it's because he's protecting himself from other predators.