I'll answer the energy one first. Heat, as a concept of energy, has been known since as long as people have had a concept of energy. What heat is we take as the average kinetic energy of movement and of vibration of particles, regardless of what phase of matter these particles are in (i.e. solid, liquid, gas, or plasma). It thus applies to any moving or vibrating particle, which can be a molecule, an atom, or even a subatomic particle such as an unbound electron in plasma. In a gas or plasma, the movement of these particles continually impacting the sides of the container they are in and against each-other exerts a pressure, a continual force per unit area. It is this pressure that drives nearly all kinds of mechanical engines, including steam engines.

The way that a steam engine works is by having a reservoir of water which is heated, causing it to boil, transforming it into a gas, which exerts the mentioned pressure. The chamber in which the water vapor is contained has an outlet for the gas to escape into the lower pressure (and lower temperature) air outside of the engine, but to do so, it must push a piston out of the way (and, because the piston is attached to a wheel, pushing out that piston releases some of the steam before a new piston slides into place). The piston is itself connected to a motor or wheel of some sort, so that moving the piston turns the wheel. Thus, steam escaping from the boiler drives the boat forward.

Because warm air exerts more pressure back on the piston to hold the steam in, the engine will run more efficiently if the air is colder. The water the boat is sitting in however does not make much difference.