1 They usually do more damage with the first damage type, that is considered primary, the other one secondary. You usually rely on the first damage type, the second one is just a.. nice boon to have, but nothing essential.
2 Exactly, Hull Health is the armor, the upper white bar on the Hull when ingame, the one you can repair. Ship health is the lower, yellow bar that gets damaged when the Armor is down and cannot be repaired. Piercing damage (Gatling, Mercury Field Gun) takes down the Armor, Explosive (Flak guns) the Health
3: Because of their higher maneuverability. A big ship is of no use if it can't catch up with the small one. And the small ships don't have so many weapon slots or options, so they have to use them on close range on enemy blind spots to make a difference. They simply don't do enough damage from afar - AND the big ships can always shoot back, chances are, the small ship gets hit and can't take the damage, while the big ship can easily take loads of damage without flinching.
4 The front horns are purely aesthetic, I think. They're good for ramming because they have a gun at the front; that means you can fire while going in for the ram without worrying about positioning your ship right or anything like that. Also, they have the necessary speed and maneuverability for ramming. A galleon is just too slow to ram, and it doesn't have guns at the front.
5. That purely depends on the enemy crews. If you've got a enemy spire that isn't even firing, it'll die in a second and is a very easy kill. You could take those down while getting fired at by the other enemy ship. Then, a Galleon with short range weaponry on the other side of the map isn't a threat, you can ignore them until they get into firing range, and so on. What usually works though is focusing on the weakest ship in terms of hull health and so on, hoping for a easy kill before you close in with the bigger enemy ships.
6. The 2 side Engines are indeed responsible for turning, if you've got one of them destroyed, you can only fly in circles, for example.
7. The Targetsquare is called a Spot and can be made using the Pilot's tool (also available to the other classes) Spyglass! It disappears when the enemy ship is "out of sight", meaning behind an obstacle you can't see trough, very far away, or in clouds.