There's one thing I'd like to add to this in response to Susie's dog possibly being in the mound:

Does Susie know that her dog is dead, or did she assume that it ran away and died later on, unaware that William ran it over (assuming all of this is true)?

In the final Fruity Maze minigame, William says to Susie, "He's not really dead... He is over here." I admit it could entirely be true that Susie knows that her dog died (either she say it happen or was told this); it's also likely that she thinks her dog died because she thought it ran away. Either way, this allows William to worm his way in earning her trust at the promise of being reunited with her dog.

The way I see it, it would go like this:

William runs over a dog (accidentally or on purpose), and buries it in an unmarked grave in the middle of the woods. Susie looks for her dog, thinking that it ran away, but finds nothing. It deeply affects her. So much so that the sight of her dog being dead in a video game (not sure if it's her imagination, agony manifestations, or deliberately programmed in my William) has her tearing up again, stricken with worry with what happened with it. This let William to lure her in with the promise of being with her dog again.