The reason you need to boil melted water is to get rid of microorganisms and impurities that make it unsafe for consumption. Since melted water is mostly from snow, ice caps glaciers etc that must have been scooped from around the environment. Some people even add chlorine and other disinfectant to keep it clean.
Snow and rain water absorb all the dust, bacteria, spores, stinky gases, whatever out of the sky while falling, so you really should purify the melt water before drinking it. Water that soaks through sand or has flowed in a stream is clean.
No, it's not necessary to boil water before freezing it. Boiling water kills bacteria and viruses, but freezing can also effectively kill some of them.
Melted water is simply water that has transitioned from a frozen state to a liquid state due to an increase in temperature. Boiling water before freezing is not necessary; in fact, it's the opposite process. Boiling removes impurities and gases, and freezing results in the water returning to a solid state. If you're concerned about water quality, it's more common to purify water before drinking rather than boiling it before freezing.