  [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.
