Magnetic fields are an important ingredient of the interstellar medium (ISM). Besides their importance for star formation, they govern the transport of cosmic rays, relevant to the launch and regulation of galactic outflows and winds, which in turn are pivotal in shaping the structure of halo magnetic fields. Mapping the small-scale structure of interstellar magnetic fields in many nearby galaxies is crucial to understand the interaction between gas and magnetic fields, in particular how gas flows are affected. Elucidation of the magnetic role in, e.g., triggering star formation, forming and stabilising spiral arms, driving outflows, gas heating by reconnection and magnetising the intergalactic medium has the potential to revolutionise our physical picture of the ISM and galaxy evolution in general. Radio polarisation observations in the very nearest galaxies at high frequencies (>= 3 GHz) and with high spatial resolution (<= 5") hold the key here. The galaxy survey with SKA1 that we propose will also be a major step to understand the galactic dynamo, which is important for models of galaxy evolution and for astrophysical magnetohydrodynamics in general. Field amplification by turbulent gas motions, which is crucial for efficient dynamo action, has been investigated so far only in simulations, while compelling evidence of turbulent fields from observations is still lacking.