We present a detailed study of the optical spectroscopic properties of 12 active galactic nuclei (AGNs) with candidate low-mass black holes (BHs) selected by Kamizasa et al. through rapid X-ray variability. The high-quality, echellette Magellan spectra reveal broad Hα emission in all the sources, allowing us to estimate robust virial BH masses and Eddington ratios for this unique sample. We confirm that the sample contains low-mass BHs accreting at high rates: the median MBH = 1.2 × 106 M☉ and median Lbol/LEdd = 0.44. The sample follows the MBH-σ* relation, within the considerable scatter typical of pseudobulges, the probable hosts of these low-mass AGNs. Various lines of evidence suggest that ongoing star formation is prevalent in these systems. We propose a new strategy to estimate star formation rates in AGNs hosted by low-mass, low-metallicity galaxies, based on modification of an existing method using the strength of [O II] λ3727, [O III] λ5007, and X-rays.