This paper presents a broad theoretical and simulation study of the high temperature behavior of crystalline alkali halide surfaces typified by NaCl(100), of the liquid NaCl surface near freezing, and of the very unusual partial wetting of the solid surface by the melt. Simulations are conducted using two-body rigid ion BMHFT potentials, with full treatment of long-range Coulomb forces. After a preliminary check of the description of bulk NaCl provided by these potentials, which seems generally good even at the melting point, we carry out a new investigation of solid and liquid surfaces. Solid NaCl(100) is found in this model to be very anharmonic and yet exceptionally stable when hot. It is predicted by a thermodynamic integration calculation of the surface free energy that NaCl(100) should be a well ordered, non-melting surface, metastable even well above the melting point. By contrast, the simulated liquid NaCl surface is found to exhibit large thermal fluctuations and no layering order. In spite of that, it is shown to possess a relatively large surface free energy. The latter is traced to a surface entropy deficit, reflecting some kind of surface short range order. Finally, the solid-liquid interface free energy is derived through Young's equation from direct simulation of partial wetting of NaCl(100) by a liquid droplet. It is concluded that three elements, namely the exceptional anharmonic stability of the solid (100) surface, the molecular short range order at the liquid surface, and the costly solid liquid interface, all conspire to cause the anomalously poor wetting of the (100) surface by its own melt in the BMHFT model of NaCl -and most likely also in real alkali halide surfaces.