  (abidged) Context: Stellar convection zones are characterized by vigorous
high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the
dynamo and differential rotation regimes at varying levels of viscous, thermal,
and magnetic diffusion. Methods: We perform three-dimensional simulations of
stratified fully compressible magnetohydrodynamic convection in rotating
spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to
2 and 5, respectively). Results: We find that the rotation profiles for high
thermal diffusivity show a monotonically increasing angular velocity from the
bottom of the convection zone to the top and from the poles toward the equator.
For sufficiently rapid rotation, a region of negative radial shear develops at
mid-latitudes as the thermal diffusivity is decreased. This coincides with a
change in the dynamo mode from poleward propagating activity belts to
equatorward propagating ones. Furthermore, the cyclic solutions disappear at
the highest magnetic Reynolds numbers. The total magnetic energy increases with
the magnetic Reynolds number in the range studied here ($5-151$), but the
energies of the mean magnetic fields level off at high magnetic Reynolds
numbers. The differential rotation is strongly affected by the magnetic fields
and almost vanishes at the highest magnetic Reynolds numbers. In some of our
most turbulent cases we find that two regimes are possible where either
differential rotation is strong and mean magnetic fields relatively weak or
vice versa. Conclusions: Our simulations indicate a strong non-linear feedback
of magnetic fields on differential rotation, leading to qualitative changes in
the behaviors of large-scale dynamos at high magnetic Reynolds numbers.
Furthermore, we do not find indications of the simulations approaching an
asymptotic regime where the results would be independent of diffusion
coefficients.
