The ship is moving a lot faster than it looks in the film and if down at sea level and from a distance, it can be deceiving how fast they are moving.
As to why it hit the ship, the coxswain probably had that many things going on like ducking bullets, trying t keep the speed up, crossing the bow waves (which wouldn't be small on a ship that size), he probably just "lost it".
I think the boat being shot at at the rear of the ship is the same boat as the one at the beginning of the film. Once it hit the side of the ship, it would not take long (10 - 15 seconds at most) for it to be passed by and spat out the back.
As to boarding a ship of that size at that speed, well I reckon you would have to have whatever system you use down pat and that is if you had any decent system at all as opposed to throwing a rope / grappling hook and climbing.