Recent discovery of the anomalous crystallization in n-alkanes and n-alcohols at the free surfaces of melts has revealed the necessity for much deeper understanding of the molecular mechanism of crystallization. With the aid of large-scale molecular simulation, and by use of a simplified molecular model of bead spring, the molecular processes of melting and crystallization in a thin film of n-alkane are directly observed. It is found that melting of the thin film is greatly influenced by its surface state. The film is more stable when the surface chains are lying perpendicular to the surface, on which the chain ends have marked preference. Crystallization by both rapid and slow cooling of the melt is shown to give rise to a formation of monolayers on the free surfaces. By slow stepwise cooling, the layer-by-layer growth of stacked lamellae is clearly reproduced. Detailed inspection of the molecular processes involved shows that there are considerable differences in the molecular mechanisms of monolayer formation and 3D crystallization. Furthermore, the molecular mobility and diffusivity in the surface monolayer are discussed. It is shown that longitudinal displacements of the chains along their axes are much larger in the monolayer than in the crystals, and that the calculated rate of transverse diffusion in the monolayer shows good comparison with experimental values. The interchanges of the molecules between the melt and the surface monolayers are observed directly; dynamical stability of the surface monolayer is clearly demonstrated.