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 H$alpha$ emission in all the sources, allowing us to estimate robust viral BH masses and Eddington ratios for this unique sample. We confirm that the sample contains low-mass BHs accreting at high rates: the median $M_{rm BH} = 1.2times 10^6M_odot$ and median $L_{rm bol}/L_{rm Edd}=0.44$. The sample follows the $M_{rm BH}-sigma_*$ 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] $lambda 3727$, [O III] $lambda 5007$, and X-rays.
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