SPHERE/ZIMPOL observations of the symbiotic system R Aquarii. II. Dynamics of the dust in the Mira wind and the Hα gas in the jet

R Aqr is a resolved symbiotic Mira binary and a prototype target for the study of complex hydrodynamic processes including dust-driven mass loss, mass transfer, accretion, and jet outflows and the formation of strongly asymmetric circumstellar structures. With the aim of gaining a better understanding of the complex hydrodynamics of R Aqr, we conducted an investigation based on new high-resolution imaging of the Hα emission from the ionized gas and of the polarization from scattering dust. We analyzed SPHERE/ZIMPOL Hα and polarization maps with a resolution of ≈ 25 mas (5 AU) for the innermost region -- rłapprox 2'' (łapprox 400 AU) -- of the R Aqr system. Data for four epochs were taken covering 6.7 years, including the dust eclipse phase around 2021, providing the angular motion and structural changes for the Hα and dust clouds, which are measured and described in detail. The results are compared with literature data and put into context with respect to models for AGB star binaries. The central Hα emission traces the orbital motion of the hot component. The circumstellar polarization from scattering dust shows interaction effects near the binary (łapprox 60 AU), including a flattened distribution aligned with the orbital plane, corotating dust, and a reduction of the scattering signal during the dust eclipse phase. The polarization shows for gapprox 60 AU a steady outflow with about a dozen dust clouds, a few of which have a comet-like core and tail features. The dust velocity is about 20 km,s ^ -1 , and this is faster than for the CO gas measured with ALMA. Several prominent Hα clouds near the binary (łapprox 200 AU) also show scattering polarization because they are just partly ionized dust clouds from the Mira wind. We also found small faster-moving transient Hα clouds, pointing to outflow instabilities such as those in clumpy winds of hot stars. The observed temporal changes of the Hα emission, in particular the overall angular shift during the dust eclipse event, can be explained by strong illumination changes from the hot component. At a larger separation (gapprox 500 AU), the Hα clouds move faster ($>100 km,s ^ -1 $), in agreement with previous studies. This acceleration in the outflow is probably a result of gas heating by photoionization and shocks in the clumpy outflow, and the produced overpressure gives rise to the two well-known jet-like features expanding in polar directions. Monitoring of the inner regions of R Aqr shows the motion and evolution of different structures in the dusty Mira wind and the ionized outflow of the hot component, and these features provide unambiguous information about the hydrodynamics of the circumstellar material. Such observations are very useful to clarify the complex phenomena taking place in interacting binaries with asymptotic giant branch stars.