How to find the Cp, difference of Cp and heat of fusion from the dependence of vapor pressure on temperature?
Use the equation for the vapor pressure of the solid to get the heat of sublimation.  The heat capacity of the vapor minus the heat capacity of the liquid is equal to the derivative of the heat of vaporization with respect to temperature. The heat capacity of the vapor minus the heat capacity of the solid is equal to the derivative of the heat of sublimation with respect to temperature.

ADDENDUM

$$\Delta H_{sublimation}=RT^2\frac{d\ln{P}}{dT}=(\ln{10})RT^2\frac{d\log{P}}{dT}$$where log P is given by Eqn. 1.