Benzene is more stable because it contains a ring and therefore an aromatic compound. On the other hand, 1,3,5-hexatriene, as a straight-chain alkene, is aliphatic. Aromatic compounds in general are more stable than their aliphatic counterparts because pi electrons are part of a conjugated system, meaning they are "shared" amongst all double-bonded atoms.
In the context of chemistry, yes. Energy input is always equal to the energy output.
the solid particles take up the intermolecular spaces in the liquid.