Thermodynamic quantities for the freezing of water
s is not correct because U is not just a function of temperature but also a function of chemical composition.  The internal energy of liquid water is higher than the internal energy of ice.  If you want to think of it in terms of temperature, then just view the heat capacity as being infinite at the phase transition (Dirac delta function of T), such that the integral over the phase change is equal to the heat of fusion.  As far as q is concerned, I guess they are assuming that the change in volume from solid to liquid is negligible.