The Kepler mission has delivered unprecedented high-quality photometry. These data have impacted numerous research fields including Galactic studies, asteroseismology, and exoplanets, and continue to be an astrophysical gold mine to this day. Because of this, thorough investigations of the ∼200,000 stars observed by Kepler remain of paramount importance. In this work, we present three aspects of a state-of-the-art characterization of the Kepler targets based on Gaia DR3. First, we report several categories of candidate binary systems spanning a range of detection methods, such as Renormalised Unit Weight Error (RUWE), radial-velocity variables, Gaia non-single stars (NSS), and eclipsing binaries. Second, we investigate the color-magnitude diagram (CMD), and classify stars into several CMD categories (dwarfs, subgiants, red giants, among others). Third, we use the Gaia DR3 astrometry to perform a detailed kinematic analysis. We classify the Kepler-field stars according to different Galactic components (thin disk, thick disk, halo), and approximately triple the sample size of previous works. We explore the role of their Galactic population membership in properties such as stellar rotation, asteroseismic ages, and chemical composition. Our multi-dimensional analysis will constitute a valuable resource for future research on the Kepler stars and their planets, and highlights the capabilities of combining the Gaia data with photometric missions such as TESS and the upcoming PLATO.