  We present exoplanet occurrence rates estimated with approximate Bayesian
computation for planets with radii between 0.5 and 16 $R_{\bigoplus}$ and
orbital periods between 0.78 and 400 days, orbiting FGK dwarf stars. We base
our results on an independent planet catalogue compiled from our search of all
~200,000 stars observed over the Kepler mission, with precise planetary radii
supplemented by Gaia DR2-incorporated stellar radii. We take into account
detection and vetting efficiency, planet radius uncertainty, and reliability
against transit-like noise signals in the data. By analyzing our FGK occurrence
rates as well as those computed after separating F-, G-, and K-type stars, we
explore dependencies on stellar effective temperature, planet radius, and
orbital period. We reveal new characteristics of the photoevaporation-driven
"radius gap" between ~1.5 and 2 $R_{\bigoplus}$, indicating that the bimodal
distribution previously revealed for $P$ < 100 days exists only over a much
narrower range of orbital periods, above which sub-Neptunes dominate and below
which super-Earths dominate. Finally, we provide several estimates of the
"eta-Earth" value -- the frequency of potentially habitable, rocky planets
orbiting Sun-like stars. For planets with sizes 0.75 - 1.5 $R_{\bigoplus}$
orbiting in a conservatively defined habitable zone (0.99 - 1.70 AU) around
G-type stars, we place an upper limit (84.1th percentile) of <0.18 planets per
star.
