Frozen Lake
No. It loses thermal energy.
No, liquid particles lose energy when frozen, everything loses energy when frozen and their molecular movement slows down. Their is a state called 0 degrees Kelvin which is the lowest temperature possible. At 0 degrees Kelvin all molecular motion is stopped and all energy is lost. Liquids would gain energy when heated.
Boiling.
No. You will be boiling hot in fact! You won't be frozen, you will be boiled.
No. That raises the temperature too high.
The energy must be applied to the phase change before it can heat the substance
"Wave energy" can be a lot of things, you need a more specific question. Energy that travels in "waves" includes a lot of things such as: Radiation, thermal energy, even matter (which has both a wave length and unless frozen, has energy). So... no natural gas is not more available then "wave energy".
melted
europa
Because energy is related to the Atomic Mass of the substance (1/2 mv^2 and all that). So, at the same temperature a more massive substance has a greater thermal energy.
Ice contains H2o in a frozen state.
cryosphere