Context: Stellar convection zones are characterized byvigorous high-Reynolds number turbulence at low Prandtl numbers. Aims:We study the dynamo and differential rotation regimes at varying levelsof viscous, thermal, and magnetic diffusion. Methods: We performthree-dimensional simulations of stratified fully compressiblemagnetohydrodynamic convection in rotating spherical wedges at variousthermal and magnetic Prandtl numbers (from 0.25 to 2 and 5,respectively). Results: We find that the rotation profiles for highthermal diffusivity show a monotonically increasing angular velocityfrom the bottom of the convection zone to the top and from the polestoward the equator. For sufficiently rapid rotation, a region ofnegative radial shear develops at mid-latitudes as the thermaldiffusivity is decreased. This coincides with a change in the dynamomode from poleward propagating activity belts to equatorward propagatingones. Furthermore, the cyclic solutions disappear at the highestmagnetic Reynolds numbers. The total magnetic energy increases with themagnetic Reynolds number in the range studied here ($5-151$), but theenergies of the mean magnetic fields level off at high magnetic Reynoldsnumbers. The differential rotation is strongly affected by the magneticfields and almost vanishes at the highest magnetic Reynolds numbers. Insome of our most turbulent cases we find that two regimes are possiblewhere either differential rotation is strong and mean magnetic fieldsrelatively weak or vice versa. Conclusions: Our simulations indicate astrong non-linear feedback of magnetic fields on differential rotation,leading to qualitative changes in the behaviors of large-scale dynamosat high magnetic Reynolds numbers. Furthermore, we do not findindications of the simulations approaching an asymptotic regime wherethe results would be independent of diffusion coefficients.