We present gas-phase metallicity measurements for 583 emission line galaxies at 0.3<z<0.85, including 388 dwarf galaxies with log(M_*_/M_{sun}_)<9.5, and explore the dependence of the metallicity on the stellar mass and star formation (SF) properties of the galaxies. Metallicities are determined through the measurement of emission lines in very deep (~7hr 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 [NeIII]{lambda}3869 and [OIII]{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~0 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 (SFR). 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 [OII]{lambda}{lambda}3727,3729 doublet to calculate gas electron density in ~1000 galaxies with log(M_*_/M_{sun}_)<10.5 as a function of redshift. We measure low electron densities (n_e_~25cm^-3^) for z<1 galaxies, again consistent with z~0 conditions, but measure higher densities (n_e_~100cm^-3^) at z>1. These results all suggest that there is little evolution in star-forming interstellar medium conditions from z~1 to z=0, confirmed with a more complete sample of low-mass galaxies than has previously been available in this redshift range.