  [Abridged] Ensemble studies of red-giant stars with exquisite asteroseismic,
spectroscopic, and astrometric constraints offer a novel opportunity to recast
and address long-standing questions concerning the evolution of stars and of
the Galaxy. Here, we infer masses and ages for nearly 5400 giants with
available Kepler light curves and APOGEE spectra, and discuss some of the
systematics that may affect the accuracy of the inferred stellar properties.
First, we look at age-chemical-abundances relations. We find a dearth of young,
metal-rich stars, and the existence of a significant population of old (8-9
Gyr), low-[$\alpha$/Fe], super-solar metallicity stars, reminiscent of the age
and metallicity of the well-studied open cluster NGC6791. The
age-chemo-kinematic properties of these stars indicate that efficient radial
migration happens in the thin disk. We find that ages and masses of the nearly
400 $\alpha$-element-rich red-giant-branch (RGB) stars in our sample are
compatible with those of an old (~11 Gyr), nearly coeval, chemical-thick disk
population. Using a statistical model, we show that 95% of the population was
born within ~1.5 Gyr. Moreover, we find a difference in the vertical velocity
dispersion between low- and high-[$\alpha$/Fe] populations, confirming their
different chemo-dynamical histories. We then exploit the almost coeval
$\alpha$-rich population to gain insight into processes that may have altered
the mass of a star along its evolution, which are key to improve the mapping of
the observed stellar mass to age. We find evidence for a mean integrated RGB
mass loss <$\Delta$M>= 0.10 $\pm$ 0.02 Msun and that the occurrence of massive
(M $\gtrsim$ 1.1 Msun) $\alpha$-rich stars is of the order of 5% on the RGB,
and significantly higher in the RC, supporting the scenario in which most of
these stars had undergone interaction with a companion.
