  Studies of exoplanet demographics require large samples and precise
constraints on exoplanet host stars. Using the homogeneous Kepler stellar
properties derived using Gaia Data Release 2 by Berger et al. (2020), we
re-compute Kepler planet radii and incident fluxes and investigate their
distributions with stellar mass and age. We measure the stellar mass dependence
of the planet radius valley to be $d \log R_{\mathrm{p}}$/$d \log M_\star =
0.26^{+0.21}_{-0.16}$, consistent with the slope predicted by a planet mass
dependence on stellar mass ($0.24-0.35$) and core-powered mass-loss (0.33). We
also find first evidence of a stellar age dependence of the planet populations
straddling the radius valley. Specifically, we determine that the fraction of
super-Earths ($1-1.8 \mathrm{R_\oplus}$) to sub-Neptunes ($1.8-3.5
\mathrm{R_\oplus}$) increases from $0.61 \pm 0.09$ at young ages (< 1 Gyr) to
$1.00 \pm 0.10$ at old ages (> 1 Gyr), consistent with the prediction by
core-powered mass-loss that the mechanism shaping the radius valley operates
over Gyr timescales. Additionally, we find a tentative decrease in the radii of
relatively cool ($F_{\mathrm{p}} < 150 \mathrm{F_\oplus}$) sub-Neptunes over
Gyr timescales, which suggests that these planets may possess H/He envelopes
instead of higher mean molecular weight atmospheres. We confirm the existence
of planets within the hot sub-Neptunian "desert" ($2.2 < R_{\mathrm{p}} < 3.8
\mathrm{R_\oplus}$, $F_{\mathrm{p}} > 650 \mathrm{F_\oplus}$) and show that
these planets are preferentially orbiting more evolved stars compared to other
planets at similar incident fluxes. In addition, we identify candidates for
cool ($F_{\mathrm{p}} < 20 \mathrm{F_\oplus}$) inflated Jupiters, present a
revised list of habitable zone candidates, and find that the ages of single-
and multiple-transiting planet systems are statistically indistinguishable.
