First, graves' interactions with crits. For normal shots, graves' shotgun shoots 4 pellets. When he crits, he shoots 8. With IE, it increases the crit bonus by 50%, in this case meaning 2 more shots for a total of 10 bullets.
Graves has a weird interaction with on-hits. Let's say Graves has
for the sake of example (DON'T EVER DO THIS ON GRAVES). Each time he shoots his shotgun, a specific target can only be hit by the bork on-hit once. So if you get hit by all 4 pellets, you still only take the 6% current hp. However, if the pellets his multiple targets in a shot, each target takes the on-hit 6% current hp, but no one takes more than that.
Fervor of battle and guinsoo's rageblade stack per auto attack, not per hit, meaning each time he autos, he will get 1 stack, and one stack only. In addition to his very mediocre application of on-hits and huge restrictions on AS (lowest base AS in the game by far, ammo system), don't build on-hits on him. Just stack AD and armor pen, maybe get an AS item (
is standard for this) for slightly better AS.
He does do more damage the closer he is, as it is a shotgun that fires 4-10 pellets (already went over this). Each pellet does damage, so getting hit by 4 pellets is more damage than just 1, and being closer to him will increase the likelyhood that you'll get hit by more than one shot in a spread.
If you have any more questions, feel free to respond to this comment, and I'll try to cover them.