LEGA-C stellar populations scaling relations. I: Chemo-archaeological downsizing trends at z~0.7

We analyze stellar population properties of 552 galaxies at redshift 0.6<z<0.77 from the LEGA-C spectroscopic survey. This first paper in a series presents the catalog of revised absorption indices for LEGA-C DR3 and inferred physical parameters, and derives benchmark scaling relations for the general massive galaxy population at intermediate redshift. We estimate light-weighted mean ages and stellar metallicities by interpreting key stellar absorption features and rizYJ photometry in a Bayesian framework with a comprehensive library of model spectra based on stochastic star formation and metallicity histories and dust attenuations. We discuss systematic uncertainties within our method and compared to other spectral fitting approaches. We derive volume-weighted scaling relations of light-weighted mean ages and stellar metallicities with stellar mass for the general galaxy population at <z>=0.7 and masses >10^10Msun. The downsizing trends observed locally were already in place 6 Gyr ago. We observe bimodal age distribution as a function of mass, transitioning around 10^11Msun. No bimodality appears in the stellar metallicity-mass relation, which changes from steep to flat across 10^10.8Msun. Similar trends emerge for age and metallicity with velocity dispersion, but with sharper transition from young to old around log(sigma)=2.3. Differences with respect to trens with stellar mass suggest that age primarily depends on velocity dispersion below and above the transition regime, while both stellar mass and velocity dispersion contribute to stellar metallicity. The catalogs of revised absorption index measurements for LEGA-C DR3 and inferred stellar population physical parameters will be released to public repositories. (Abridged)