  We present gas-phase metallicity measurements for 583 emission line galaxies
at $0.3<z<0.85$, including 388 dwarf galaxies with $log(M_{\star}/M_{\odot}) <
9.5$, and explore the dependence of the metallicity on the stellar mass and
star formation properties of the galaxies. Metallicities are determined through
the measurement of emission lines in very deep ($\sim$7 hr exposure)
Keck/DEIMOS spectra taken primarily from the HALO7D survey. We measure
metallicity with three strong-line calibrations (O3H$\beta$, R23, and O3O2) for
the overall sample, as well as with the faint [Ne III]$\lambda$3869 and [O
III]$\lambda$4363 emission lines for 112 and 17 galaxies where robust
detections were possible. We construct mass-metallicity relations (MZR) for
each calibration method, finding MZRs consistent with other strong-line results
at comparable redshift, as well as with $z\sim0$ galaxies. We quantify the
intrinsic scatter in the MZR as a function of mass, finding it increases with
lower stellar mass. We also measure a weak but significant correlation between
increased MZR scatter and higher specific star formation rate. We find a weak
influence of SFR in the fundamental metallicity relation as well, with an SFR
coefficient of $\alpha=0.21$. Finally, we use the flux ratios of the [O
II]$\lambda\lambda$3727,3729 doublet to calculate gas electron density in
$\sim$1000 galaxies with $log(M_{\star}/M_{\odot}) < 10.5$ as a function of
redshift. We measure low electron densities ($n_e\sim25$ cm$^{-3}$) for $z<1$
galaxies, again consistent with $z\approx0$ conditions, but measure higher
densities ($n_e\sim100$ cm$^{-3}$) at $z>1$. These results all suggest that
there is little evolution in star-forming interstellar medium conditions from
$z\sim1$ to $z=0$, confirmed with a more complete sample of low-mass galaxies
than has previously been available in this redshift range.
