[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.