  Upon its release the Gaia DR3 catalogue has led to tremendous progress in
multiple fields of astronomy by providing the complete astrometric solution for
nearly 1.5 billion sources. We analysed the photometric and astrometric results
for Hydrogen-deficient Carbon (HdC), Extreme Helium (EHe), and DYPer type stars
to identify any potential biases and thus to select stars suitable for
kinematic and spatial distribution studies. We investigated the impact of
photometric declines in R Coronae Borealis (RCB) stars on Gaia astrometry using
information from the Gaia IPD process cross-matched with light curves. We have
reached the conclusion that the astrometric fits for numerous RCB stars are not
valid due to the Gaia PSF chromaticity effect in both shape and centroid. The
astrometric results of all stars with a significant time-dependent colour
variation should be similarly affected. RCB stars might thus be promising
sources to correct this effect in future Gaia releases. Furthermore, after
validating the Gaia astrometric results for 92 stars, we observed that the
majority of HdC and EHe stars are distributed across the three old stellar
structures, the thick disk, the bulge and the halo. However, we have also
uncovered evidence indicating that some of them exhibit orbits characteristic
of the thin disk. This is also particularly true for all DYPer type stars
studied. Finally, we have produced a list of star memberships for each Galactic
substructure, and provided a list of heliocentric radial velocities and
associated errors for targets not observed by Gaia DR3. We are beginning to
observe a relationship between kinematics, stellar population, and metallicity
in RCB and EHe stars. That relation can be explained, within the double
degenerate scenario, by the large range in the delay time distribution expected
from population synthesis simulations, particularly through the HybCO merger
channel.
