We discuss the results of a molecular dynamics (MD) study of the residence times of water in the primary hydration shells of ions and uncharged solutes at infinite dilution in supercritical water at 683 K, as well as the solvation dynamics and diffusion coefficients of these species. The SPC/E model is used to represent water in this paper and its companion, where structural aspects of the same systems are discussed. The residence times at 683 K are found to be lower than those under ambient conditions and only weakly dependent on the size and sign of the charge on the ions. In contrast to earlier studies at room temperature (298 K at a solvent density of 0.997 g cm(-3)), the solvation dynamics of sodium and chloride ions at 683 K and a solvent density of 0.35 g cm(-3) are very similar to each other and indicate a solvent relaxation time of 0.8 ps. The ion diffusion coefficients are larger in magnitude at 683 K and less differentiated by size and charge sign at low solvent density (less than or equal to0.35 g cm(-3)) than they are at room temperature. In the low-density range, an uncharged solute of the same size as an ion diffuses 2-9 times faster than the corresponding charged species, with the smaller solutes moving much faster than the larger ones. Increasing the solvent density to 0.997 g cm(-3) at 683 K decreases the diffusion coefficients of ions and uncharged solutes. At this density, the diffusion coefficients pass through distinct maxima as a function of size at both 298 and 683 K. An explanation of the diffusion coefficients of charged and uncharged species at low solvent density is sought in terms of a semicontinuum theory. The importance of the time scale of the solvent density fluctuations in controlling diffusion as distinct from the spatial extent of these fluctuations (determined by the correlation length) is emphasized. These observations suggest that the mechanisms of solute diffusion at supercritical conditions and at room temperature may be fundamentally different.