1) To submerge, the submarine fills what are called ballast tanks with water, thereby increasing the "density" of the vessel causing it to sink. When they want to raise the ship, the fill the tanks with air, thereby decreasing the density of the vessel enough to cause it to raise up.

2) Yes. Because when laying down, the log is at equilibrium, the forces must be balanced and because the mass hasn't changed, neither can the buoyant force. However, the components of the buoyant force equation are different . When horizontal, the cross sectional area is huge, but the height is small. When vertical, although the cross sectional area is small, that is made up for with the height that it sinks, as it will sink much lower. But the force itself is the same.

3) No. Although there is an upward buoyant force acting on the block, there is an equal and opposite force directed down on the water. Therefore this is as if extra mass was just added to the system.

4)  This problem is based on the shortcut method for these problems which is written .  Therefore 

5) Yes, because buoyant force is dependent upon nothing but the density of the fluid, gravity, the cross sectional area and the height, they will have the same buoyant force