We study the population of Galactic planetary nebulae (PNe) and their central stars (CSs) through the analysis of their distances and Galactic distribution. The PN distances are obtained by means of a revised statistical distance scale, based on an astrometrically-defined sample of CSs from Gaia DR3 as calibrators. The new statistical distances, together with the proper motion of the CSs - also from DR3, and with published PN abundances as well as radial velocities, are used to characterize the PN populations in the Galaxy, and to derive the radial metallicity gradient. The statistical scale is applied to infer distances of a significant number (~850) of Galactic PNe, for which we deliver a new catalog of PN distances. By adopting a circular velocity curve of the Galaxy, we also obtain peculiar 3D velocities for a large sample of PNe (~300). Elemental abundances of the PNe are culled from the literature for an updated catalog, to be used in our analysis and other external applications. The radial chemical gradient of the Galactic Disk is traced by PNe with available chemical abundances and distances, and kinematic data of the CSs are employed to identify the Halo PN population.We date PN progenitors based both on abundances and on kinematic properties, finding a confirmation of the first method with the second. For all PNe with at least one oxygen determination in the literature, we find a slope of the radial oxygen gradient equal to {DELTA}log(O/H)/{DELTA}RG=-0.0144+/-0.00385 [dex/kpc]. Furthermore, we estimate radial oxygen gradients for the PNe with old (>7.5Gyr) and young (<1Gyr) progenitors to be respectively {DELTA}log(O/H)/{DELTA}RG=-0.0121+/-0.00465 and -0.022+/-0.00758 [dex/kpc], thus disclosing a mild steepening of the gradient since Galaxy formation, with a slope change of 0.01dex. The time evolution is slightly higher (~0.015dex) if we select the best available abundances in the literature. This result is in broad agreement with previous PN results, but now based on DR3 Gaia analysis, and also in agreement with what traced by most other Galactic probes. We also find a moderate oxygen enrichment when comparing the PNe with young and old progenitors.