We estimate ages, metallicities, $alpha$-element abundance ratios and stellar initial mass functions of elliptical (E) and S0 galaxies from the MaNGA-DR15 survey. We stack spectra and use a variety of single stellar population synthesis models to interpret the absorption line strengths in these spectra. We quantify how these properties vary across the population, as well as with galactocentric distance. This paper is the first of a series and is based on a sample of pure elliptical galaxies at z $le$ 0.08. We show that the properties of the inner regions of Es with the largest luminosity (L$_r$) and central velocity dispersion ($sigma_0$) are consistent with those associated with the commonly used Salpeter IMF, whereas a Kroupa-like IMF is a better description at $sim$ 0.8R/Re (assuming [Ti/Fe] variations are limited). For these galaxies the stellar mass-to-light ratio decreases at most by a factor of 2 from the central regions to Re. In contrast, for lower L$_r$ and $sigma_0$ galaxies, the IMF is shallower and M$_{*}$/L$_r$ in the central regions is similar to the outskirts. Although a factor of 2 is smaller than previous reports based on a handful of galaxies, it is still large enough to matter for dynamical mass estimates. Accounting self-consistently for these gradients when estimating both M$_{*}$ and M$_{dyn}$ brings the two into good agreement: gradients reduce M$_{dyn}$ by $sim$ 0.2 dex while only slightly increasing the M$_{*}$ inferred using a Kroupa IMF. This is a different resolution of the M$_{*}$-M$_{dyn}$ discrepancy than has been followed in the recent literature where M$_{*}$ of massive galaxies is increased by adopting a Salpeter IMF while leaving Mdyn unchanged. A companion paper discusses how stellar population differences are even more pronounced if one separates slow from fast rotators.
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