Burying (or not burying) waste is an instinctual behavior. You might be able to create an environment that facilitates the behavior you're looking for, but you're not going to teach a cat to do it the way you want. It may be that no reasonable accommodation will make your cat actually bury his waste properly. 

**First off, check for medical issues.**

You mentioned the cat runs from the box, which sometimes cats will do if eliminating is painful, or the box has associations with pain. Examine the quality of its stool (ideally when fresh), to see if it looks too wet or too dry, which are indications of diarrhea or constipation. I would also bring it up on the next vet visit. But, on the other hand, sometimes cats run from the litterbox for no apparent reason too.

**Watch your cat when he goes.**

With any luck, you might notice something about the way the cat uses the box that helps you identify the root cause of the problem. Look for how easy is it for the cat to move and turn around while in the box, and also if there's any hesitation while using it, which could be an indication of dislike or pain.  For the peeing problem, it may even be that the cat tends to stand while peeing, which some cats do for some reason. At any rate, based on your observations, try applying the following suggestions accordingly. 

* **A bigger box.** Sometimes cats want a *much* bigger box, and honestly, there isn't all that much size variation in litterboxes, so you might try improvising one. Many people that go this route use a large Tupperware container with an entrance hole cut out. 
* **Different litter.** Some cats have sensitive paws, and so it hurts to step on larger granules. Therefore rather than trying litters randomly, I would try the finest gained litter you can find. If you suspect the litter is the problem, I recommend experimenting with no peewee at all as the granules appear quite big. 
* **Make sure you aren't using too little or too much litter.** Two to three inches is recommended, though some cats might want more or less. 
* **Clean the box much more frequently.**

The problem of peeing outside the box can probably be fixed by switching to a litterbox with very high sides or a lid, though ideally, if there's some sort of root cause that's making him not like the box, leading to his peeing over the side, that should be addressed as well.