  In this fourth paper of the series, we use the parametrized, spherically
symmetric explosion method PUSH to perform a systematic study of two sets of
non-rotating stellar progenitor models. Our study includes pre-explosion models
with metallicities Z=0 and Z=Z$_{\odot}\times 10^{-4}$ and covers a progenitor
mass range from 11 up to 75 M$_\odot$. We present and discuss the explosion
properties of all models and predict remnant (neutron star or black hole) mass
distributions within this approach. We also perform systematic nucleosynthesis
studies and predict detailed isotopic yields as function of the progenitor mass
and metallicity. We present a comparison of our nucleosynthesis results with
observationally derived $^{56}$Ni ejecta from normal core-collapse supernovae
and with iron-group abundances for metal-poor star HD~84937. Overall, our
results for explosion energies, remnant mass distribution, $^{56}$Ni mass, and
iron group yields are consistent with observations of normal CCSNe. We find
that stellar progenitors at low and zero metallicity are more prone to BH
formation than those at solar metallicity, which allows for the formation of
BHs in the mass range observed by LIGO/VIRGO.
