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We present the second catalog and data release of optical spectral line measurements and AGN demographics of the BAT AGN Spectroscopic Survey, which focuses on the of Swift-BAT hard X-ray detected AGNs. We use spectra from dedicated campaigns and publicly available archives to investigate spectral properties of most of the AGNs listed in the 70-month Swift-BAT all-sky catalog; specifically, 743 of the 746 unbeamed and unlensed AGNs (99.6%). We find a good correspondence between the optical emission line widths and the hydrogen column density distributions using the X-ray spectra, with a clear dichotomy of AGN types for NH = 10^22 cm-2. Based on optical emission-line diagnostics, we show that 48%-75% of BAT AGNs are classified as Seyfert, depending on the choice of emission lines used in the diagnostics. The fraction of objects with upper limits on line emission varies from 6% to 20%. Roughly 4% of the BAT AGNs have lines too weak to be placed on the most commonly used diagnostic diagram, [O III]λ5007/H\b{eta} versus [N II]λ6584/Hα, despite the high signal-to-noise ratio (S/N) of their spectra. This value increases to 35% in the [O III]λ5007/[O II]λ3727 diagram, owing to difficulties in line detection. Compared to optically-selected narrow-line AGNs in the Sloan Digital Sky Survey, the BAT narrow-line AGNs have a higher rate of reddening/extinction, with Hα/H\b{eta} > 5 (~ 36%), indicating that hard X-ray selection more effectively detects obscured AGNs from the underlying AGN population. Finally, we present a subpopulation of AGNs that feature complex broad-lines (34%, 250/743) or double-peaked narrow emission lines (2%, 17/743).