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We present the cold neutral content (H I and C I gas) of 13 quasar 2175 \AA$$ dust absorbers (2DAs) at $z$ = 1.6 - 2.5 to investigate the correlationbetween the presence of the UV extinction bump with other physicalcharacteristics. These 2DAs were initially selected from the Sloan Digital SkySurveys I - III and followed up with the Keck-II telescope and the MultipleMirror Telescope as detailed in our Paper I. We perform a correlation analysisbetween metallicity, redshift, depletion level, velocity width, and explorerelationships between 2DAs and other absorption line systems. The 2DAs onaverage have higher metallicity, higher depletion levels, and larger velocitywidths than Damped Lyman-$\alpha$ absorbers (DLAs) or subDLAs. The correlationbetween [Zn/H] and [Fe/Zn] or [Zn/H] and log$\Delta$V$_{90}$ can be used asalternative stellar mass estimators based on the well-establishedmass-metallicity relation. The estimated stellar masses of the 2DAs in thissample are in the range of $\sim$ 10$^9$ to $\sim$2 $\times$ 10$^{11}$$M_{\odot}$ with a median value of $\sim$2 $\times$ 10$^{10}$ $M_{\odot}$. Therelationship with other quasar absorption line systems can be described as (1)2DAs are a subset of Mg II and Fe II absorbers, (2) 2DAs are preferentiallymetal-strong DLAs/subDLAs, (3) More importantly, all of the 2DAs show C Idetections with logN(C I) $>$ 14.0 cm$^{-2}$, (4) 2DAs can be used as moleculargas tracers. Their host galaxies are likely to be chemically enriched, evolved,massive (more massive than typical DLA/subDLA galaxies), and presumablystar-forming galaxies.

Quasar 2175 \AA$ $ dust absorbers II: Correlation analysis and relationship with other absorption line systems