Ensemble studies of red-giant stars with exquisite asteroseismic (Kepler), spectroscopic (APOGEE), and astrometric (Gaia) 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 using the code PARAM, and discuss some of the systematics that may affect the accuracy of the inferred stellar properties. We then present patterns in mass, evolutionary state, age, chemical abundance, and orbital parameters that we deem robust against the systematic uncertainties explored. First, we look at age-chemical-abundances ([Fe/H] and [alpha/Fe]) relations. We find a dearth of young, metal-rich ([Fe/H]>0.2) stars, and the existence of a significant population of old (8-9Gyr), low-[alpha/Fe], super-solar metallicity stars, reminiscent of the age and metallicity of the well-studied open cluster NGC 6791. The age-chemo-kinematic properties of these stars indicate that efficient radial migration happens in the thin disc. 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 (~11Gyr), nearly coeval, chemical-thick disc population. Using a statistical model, we show that the width of the observed age distribution is dominated by the random uncertainties on age, and that the spread of the inferred intrinsic age distribution is such that 95% of the population was born within ~1.5Gyr. Moreover, we find a difference in the vertical velocity dispersion between low- and high-[alpha/Fe] populations. This discontinuity, together with the chemical one in the [alpha/Fe] versus [Fe/H] diagram, and with the inferred age distributions, not only confirms the different chemo-dynamical histories of the chemical-thick and thin discs, but it is also suggestive of a halt in the star formation (quenching) after the formation of the chemical-thick disc. 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 improving the mapping of the current, observed, stellar mass to the initial mass and thus to the age. Comparing the mass distribution of stars on the lower RGB (R<11R_{sun}_) with those in the red clump (RC), we find evidence for a mean integrated RGB mass loss DM=0.10+/-0.02M_{sun}_. Finally, we find that the occurrence of massive (M>~1.1M_{sun}_) 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 an interaction with a companion.