  Gaia data release 2 (DR2) provides the best non-rotating optical frame
aligned with the radio frame (ICRF) thanks to the inclusion of about
half-million quasars in the 5-parameter astrometric solution. Given their
crucial diagnostic role for characterizing the properties of the celestial
reference frame, we aim to make an independent assessment of the astrometry of
quasars in DR2. We cross-match with Gaia DR2 the quasars from LQAC3, SDSS and
LAMOST, obtaining 208743 new sources (denominated as KQCG). With the quasars
already identified in DR2, we estimate the global offsets of parallaxes and
proper motions of different quasar subsets to check their astrometric
consistency. The features of the proper motion field are analyzed by means of
vectorial spherical harmonics (VSH); the scalar field of parallaxes is expanded
into spherical harmonics to investigate their spatial correlation. We find a
bias of $\sim$ $-0.030$ $mas$ in KQCG parallaxes, and a bias of $-9.1$ $\mu
as/yr$ in $\mu_{\alpha\ast}$; a $\sim$ +10 $\mu as/yr$ bias in $\mu_{\delta}$
consistently found in the entire quasar sample. The results of the VSH analysis
on different subsets indicate good agreement between them. The proper motion
field exhibits a ((-6,-5,-5) $\pm$ 1) $\mu as/yr$ rotation in the northern
hemisphere and a rotation of ((0,+1,+3) $\pm$ 1 ) $\mu as /yr$ in the southern
one. The spherical harmonics expansion of the parallax field reveals an angular
scale of systematics of $\approx$ 18 degrees with a RMS amplitude of 13
$\mu$as. The positional comparison shows that the axes of the current Gaia
Celestial Reference Frame and the ICRF2 are aligned within 30 $\mu$as.
