We have investigated diffusion and hopping processes in a cluster crystal formed from mesoscopic, ultrasoft particles. In contrast to previous contributions we have explicitly included in our investigations the microscopic solvent by using a simulation scheme that takes the induced hydrodynamic interactions into account as faithfully as possible. In our investigations we first focused on the processes of migration of the ultrasoft particles. By evaluating dynamical correlation functions we were able to demonstrate that the presence of the solvent does indeed have an important impact on the diffusion and hopping processes of the particles: this applies in particular to the diffusive behaviour, to the angular orientation of the jump events and to the spatial extents of these events. In a second set-up we have added non-cluster-forming ultrasoft particles to the system, investigating thus the impact of the solvent and that of the mutual interaction of the two species of ultrasoft particles on their respective dynamic behaviours. Our investigations clearly demonstrate, beside the expected significant role that the solvent plays in this set-up, that diffusion and the jump processes show distinct differences for the two particle species.