When an assault missile attack hits a ship, does that ship only suffer one damage, or does it suffer the dice results up to 4 hits?

Assault Missile doesn't say to cancel any dice, so your main target suffers damage like normal.

(Also, it doesn't suffer 1 extra. Only other ships near it do.)

So if there's a swarm of four ships. All are at range one of each other. If my assault missile roll is four hits and the defender is unable to cancel any, he takes 4 hits and the other three ships take 1 hit for a total of 7 damage?

So if there's a swarm of four ships. All are at range one of each other. If my assault missile roll is four hits and the defender is unable to cancel any, he takes 4 hits and the other three ships take 1 hit for a total of 7 damage?

Yep. Assault Missiles are a great swarm buster.

So if there's a swarm of four ships. All are at range one of each other. If my assault missile roll is four hits and the defender is unable to cancel any, he takes 4 hits and the other three ships take 1 hit for a total of 7 damage?

Yup.

If Lt. Blount fires an Assault Missile in that same situation and rolls all blanks then the target is "hit" but takes no damage while all of those nearby ships each suffer 1 damage.