1) Melting point (and boiling point) is determined by bond strength. That is carbon chain length, molecular weight, functional groups etc...
So you are right for number 1.
2) If something shrinks in volume the molecules are being drawn together, if this is from a increase in heat, the new length in secondary bonds is at a more stable length than at the lower temp. (Nothing to do with water content, note that many organic compounds melt bellow 0 degrees C, when water is crystalline.)
If the volume decreased from water loss, that would have to be at waters boiling point and you would be determining the melting point of an impure substance (ie a solution).