Action-derived molecular dynamics was demonstrated in the companion paper (Paper I) to be effective for the analysis of atomic surface diffusion. The method is here applied to the search of minimum-energy paths and the calculation of activation energy barriers in more complex single-adatom diffusion processes on fcc metal surfaces containing steps. Diverse diffusion routes are investigated along and across one- or two-layer steps on different surface orientations. Fundamental diffusion mechanisms near the step corners are also studied. Results are analyzed in relation to the island growth mechanism, which is of importance to surface nanoengineering.