  We present a comprehensive analysis of the damped Lya 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 damped Lya systems with z > 1.5. With
little exception, these damped Llya 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.
  We present a discussion on the nucleosynthetic history of the damped Lya
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 alpha-enrichment in the damped Lya systems at low
metallicity, an interpretation further supported by the observed O/Fe, S/Fe and
Ar/Fe ratios. We also discuss Fe-peak nucleosynthesis and the odd-even effect.
  To assess the impact of dust obscuration, we present estimates of the
dust-to-gas ratios for the damped Lya sightlines and crudely calculate dust
extinction corrections. The distribution of extinction corrections suggests 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. [significantly abridged]
