We present a comprehensive analysis of the damped Lyα (DLA) abundance database presented in the first paper of this series. This database provides a homogeneous set of abundance measurements for many elements including Si, Cr, Ni, Zn, Fe, Al, S, Co, O, and Ar from 38 DLA systems with zabs 1.5. With little exception, these DLA systems exhibit very similar relative abundances. There is no significant correlation in X/Fe with [Fe/H] metallicity, and the dispersion in X/Fe is small at all metallicity. We search the database for trends indicative of dust depletion and in a few cases find strong evidence. Specifically, we identify a correlation between [Si/Ti] and [Zn/Fe] which is unambiguous evidence for depletion. Following Hou and colleagues, we present [X/Si] abundances against [Si/H] + log N(H ) and note trends of decreasing X/Si with increasing [Si/H] + log N(H ) which argue for dust depletion. Similarly, comparisons of [Si/Fe] and [Si/Cr] against [Si/H] indicate significant depletion at [Si/H] -1 but suggest essentially dust-free damped systems at [Si/H] -1.5 dex. We present a discussion on the nucleosynthetic history of the DLA systems by focusing on abundance patterns which are minimally affected by dust depletion. We find [Si/Fe] → 0.25 dex as [Zn/Fe] → 0 and that the [Si/Fe] values exhibit a plateau of ≈0.3 dex at [Si/H] -1.5 dex. Together these trends indicate significant α-enrichment in the DLA systems at low metallicity, an interpretation further supported by the observed O/Fe, S/Fe, and Ar/Fe ratios. Comparing the relative abundances of the Fe peak elements, we identify important offsets from solar relative abundances for Cr, Ni, and Fe which suggest variations in nucleosynthesis along the Fe peak. Finally, the DLA systems exhibit a modest odd-even effect revealed by Si/Al, [Si/Al] ≈ 0.4 dex, which is significantly smaller than values observed in Galactic halo stars of comparable metallicity. These observations present strong evidence that the DLA systems and Galactic halo had different enrichment histories. To assess the impact of dust obscuration, we present estimates of the dust-to-gas ratios for the DLA sight lines and crudely calculate dust extinction corrections. The distribution of extinction corrections suggests that the effects of dust obscuration are minimal and that the population of "missing" damped systems has physical characteristics similar to the observed sample. We update our investigation on the chemical evolution of the early universe in neutral gas. The results are in good agreement with our previous work, but we emphasize two differences: (1) the unweighted and N(H I)-weighted [Fe/H] mean metallicities now have similar values at all epochs except z 3.5, where small number statistics dominate the N(H I)-weighted mean; and (2) there is no evolution in the mean [Fe/H] metallicity from z = 1.7 to 3.5 but possibly a marked drop at higher redshift. We conclude with a general discussion on the physical nature of the DLA systems. We stress the uniformity of the DLA chemical abundances which indicates that the protogalaxies identified with DLA systems have very similar enrichment histories, i.e., a nearly constant relative contribution from Type Ia and Type II supernovae. The DLA systems also show constant relative abundances within a given system, which places strict constraints on the mixing timescales of the damped systems and may pose a great challenge to the protogalactic clump scenarios favored by hierarchical galaxy formation.
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