How does a ship turn?

Another question that turned out to be not as simple as it seemed! Let's assume the ship moves along with no engine power, and the rudder is used. The resulting torque will turn the ship - which does not say anything about the direction of movement yet!

Without interaction with the surrounding water the ship would keep moving in the same direction, just an an angle. Since water resistance along the ship is much lower than across (that is, moving the ship sideways), the resulting drag force will change the direction (and amount) of the speed vector in direction of the lower resistance (that is, in the direction of the long axis of the ship).

Now the same scenario with engine power: this would work even in space. The torque turns the ship and with it, the direction of force produced by the engine. This results in a force and acceleration pointing in a different direction than the current speed vector, and the direction (and maybe amount) of the speed vector will change.

What happens if you push she ship through the water at an angle and let it go? Will it turn in the direction of movement and generate less friction, slowing down the turn, or will it turn away and experience more friction, accelerating the turn?

As described above the friction will change the direction of the speed vector. But will the ship body turn as well? If the center of mass (which is the point the ship rotates about) divides the ship in parts with equal resistance the ship will not turn. So, what if that is not the case?

I would think that a lot of mass is in the stern of the ship (engine), and that the center of mass lies within the rear half of the ship. Further I believe that the stern with its rudder creates a larger sideways friction than the bow. Since torque depends on force and distance from the center of rotation, which torque will be larger?! I don't know; it might depend on the ship!