Using a simplified mode-coupling scheme (MCS) for multicomponent Brownian dispersions, we calculate the effect of mobile salt and counterions on the tracer diffusion and sedimentation of a suspended colloidal macroion. In this scheme, potential forces and also the leading far-field hydrodynamic interactions (HI) between macroion and small electrolyte ions forming its ion atmosphere are accounted for on the basis of the many-body Smoluchowski equation. The static pair correlation functions, which are needed as input, are treated in a first step within the Debye-Huckel approximation. In this way, analytical results are derived for the time-dependent friction function, the long-time tracer diffusion coefficient, and the sedimentation velocity of the macroion as functions of the electrolyte concentration, electrolyte ion mobilities, and macroion charge. Onsager's limiting law for simple electrolytes is recovered from the MCS in the limit of vanishing macroion radius. The results of our theoretical treatment are compared with experimental data on electrolyte friction and predictions of other existing theories. Good agreement with experimental data on tracer diffusion and with Booth's theory of electrolyte friction is observed. The inclusion of HI between macroion and microions is shown to be essential for a proper description of the electrolyte friction effect.