Long story short, you would build a vehicle out of blocks. The size limits ranged up to 2048 blocks total, but I don't recall if there were any dimensional limits as well; either way, for practical reasons there was never any good reason to build really large boats since you could not see through them and they tended to block your view significantly.
Once you were satisfied with the design of your vessel, you would interact with the controller block (the ship's helm) that would create the vehicle entity. The blocks that the build was made of were recorded and removed from the world, and you would be free to travel wherever you wanted (in much the same fashion as with riding a horse.) The ship was capable of incorporating functional blocks (furnaces, piping, chests, various machinery, etc), which meant you could build yourself a small mobile base. There were historically some problems (at one point, block rotation wasn't available so things like furnaces would not turn with the boat but would stay pointed in the direction they were originally placed in-world.)
Rather than just ships, the mechanics should be more complex, such as using blueprints in order to mass-produce the same model for SMP purposes, and there should be several possible kinds of vehicles, such as wagons and submarines (Althrough sumersibles would be a more appropiate word).
Yes, there definitely should, though I would consider this more of a discussion rather than a suggestion, since it's bringing up an idea for debate/discussion rather than presenting a developed idea. I've actually made a suggestion for this a while back (click here).
I do agree that it's silly to have shipwrecks without ships. Allowing people to build ships would also increase the amount that could be done with the game, as well as increase its popularity in return. It's just not fun to have motionless ships sit there and sit there...