  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 correlation
between the presence of the UV extinction bump with other physical
characteristics. These 2DAs were initially selected from the Sloan Digital Sky
Surveys I - III and followed up with the Keck-II telescope and the Multiple
Mirror Telescope as detailed in our Paper I. We perform a correlation analysis
between metallicity, redshift, depletion level, velocity width, and explore
relationships between 2DAs and other absorption line systems. The 2DAs on
average have higher metallicity, higher depletion levels, and larger velocity
widths than Damped Lyman-$\alpha$ absorbers (DLAs) or subDLAs. The correlation
between [Zn/H] and [Fe/Zn] or [Zn/H] and log$\Delta$V$_{90}$ can be used as
alternative stellar mass estimators based on the well-established
mass-metallicity relation. The estimated stellar masses of the 2DAs in this
sample 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$^{10}$ $M_{\odot}$. The
relationship 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 preferentially
metal-strong DLAs/subDLAs, (3) More importantly, all of the 2DAs show C I
detections with logN(C I) $>$ 14.0 cm$^{-2}$, (4) 2DAs can be used as molecular
gas tracers. Their host galaxies are likely to be chemically enriched, evolved,
massive (more massive than typical DLA/subDLA galaxies), and presumably
star-forming galaxies.
