>> It turns out it’s a proper scientific discipline dedicated to the engineering of ships.
No. It is about the engineering of all sorts of things. Ships are a subset. I'd say that it covers all things that float, but that wouldn't include docks, cranes and other things that integrate with ships.
>>As containers are added the ship will sink a little and increase its draft – the distance between the bottom of the hull and the waterline.
This is the wikipedia answer. In the real world "draft" is the lowest part of the ship, which might be something other than the hull. Sailboats especially measure draft from the bottom of their keel, a thing lower than the hull. The "hull" is the watertight body and doesn't include things like keels and rudders which, while uncommon on large vessels, normally extend well below the hull's depth.