[abridged] We present optical integral field spectroscopy for a flux-limited sample of 19 QSOs at z<0.2 and spatially resolve their ionized gas properties at a physical resolution of 2-5kpc. The extended narrow line regions (ENLRs), photoionized by the radiation of AGN, have sizes of up to several kpc and correlate more strongly with the QSO continuum luminosity than with the integrated [OIII] luminosity. We find a relation of the form log(r)~(0.46+-0.04)log(L_5100), reinforcing the picture of an approximately constant ionization parameter for the ionized clouds across the ENLR. Besides the ENLR, we also find gas ionized by young massive stars in more than 50 per cent of the galaxies on kpc scales. In more than half of the sample, the specific star formation rates based on the extinction-corrected Ha luminosity are consistent with those of inactive disc-dominated galaxies, even for some bulge-dominated QSO hosts. Enhanced SFRs of up to 70Msun/yr are rare and always associated with signatures of major mergers. Comparison with the SFR based on the 60+100micron FIR luminosity suggests that the FIR luminosity is systematically contaminated by AGN emission and Ha appears to be a more robust and sensitive tracer for the star formation rate. Evidence for efficient AGN feedback is scarce in our sample, but some of our QSO hosts lack signatures of ongoing star formation leading to a reduced specific SFR with respect to the main sequence of galaxies. Based on 12 QSOs where we can make measurements, we find that on average bulge-dominated QSO host galaxies tend to fall below the mass-metallicity relation compared to their disc-dominated counterparts. While not yet statistically significant for our small sample, this may provide a useful diagnostic for future large surveys if this metal dilution can be shown to be linked to recent or ongoing galaxy interactions.
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