  (Abridged) We combine deep HST grism spectroscopy with a new Bayesian method
to derive maps of gas-phase metallicity, nebular dust extinction, and
star-formation rate for 10 star-forming galaxies at high redshift
($1.2<z<2.3$). Exploiting lensing magnification by the foreground cluster
MACS1149.6+2223, we reach sub-kpc spatial resolution and push the stellar mass
limit associated with such high-z spatially resolved measurements below
$10^8M_\odot$ for the first time. Our maps exhibit diverse morphologies,
indicative of various effects such as efficient radial mixing from tidal
torques, rapid accretion of low-metallicity gas, etc., which can affect the gas
and metallicity distributions in individual galaxies. Based upon an exhaustive
sample of all existing sub-kpc metallicity gradients at high-z, we find that
predictions given by analytical chemical evolution models assuming a relatively
extended star-formation profile in the early disk formation phase can explain
the majority of observed gradients, without involving galactic feedback or
radial outflows. We observe a tentative correlation between stellar mass and
metallicity gradient, consistent with the downsizing galaxy formation picture
that more massive galaxies are more evolved into a later phase of disk growth,
where they experience more coherent mass assembly at all radii and thus show
shallower metallicity gradients. In addition, we compile a sample of
homogeneously cross-calibrated integrated metallicity measurements spanning
three orders of magnitude in stellar mass at $z\sim1.8$. We use this sample to
study the mass-metallicity relation (MZR) and test the fundamental metallicity
relation (FMR). The slope of the observed MZR can rule out the momentum-driven
wind model at 3-$\sigma$ confidence level. We find no significant offset with
respect to the FMR, taking into account the intrinsic scatter and measurement
uncertainties.
