How do the melting points, and conductivity of molecular compounds compare to those of ionic compounds?

They are generally higher because the electronegativity difference between the constituents of an ionic compound are much greater than those in a molecular compound. Since these forces pull the atoms harder, it takes more energy to excite them and get them to change state.

for molecular compounds
within the molecules, the atoms share strong covalent bonds but between the iodine molecules, they are held together only by weak Van Der Waals' forces.

whereas in ionic compounds,
positive and negative ions are arranged such that they are held tightly together in an ionic lattice structure.

thus, it requires only a small amount of energy to break the weak bonds in molecular compounds whereas a greater amount of energy is needed to break the strong bonds in ionic compounds.
this results in higher boiling n melting points in ionic compounds.

as for conductivity,
ionic compounds do not conduct electricity in the solid state because there are not free-moving ions as they are all held together in a lattice structure.
but when it is in the molten state or in an aqueos solution, it can conduct electricity.
the water molecules can separate the positive ions from the negative ions thus there will be free moving ions to conduct electricity.

as for covalent compounds, they do not conduct electricity because they do not contain ions.
(although there are afew exceptions as in the case of graphite etc)

hope that helped