  Carbon-enhanced metal-poor (CEMP) stars span a wide range of stellar
populations, from bona fide second-generation stars to later forming stars that
provide excellent probes of, e.g., binary mass transfer. Here we analyse 11
metal-poor stars of which 10 are CEMP stars. Based on high signal-to-noise
(SNR) X-Shooter spectra, we derive abundances of 20 elements (C, N, O, Na, Mg,
Ca, Sc, Ti, Cr, Mn, Fe, Ni, Sr, Y, Ba, La, Ce, Pr, Nd, Eu). From the high SNR
spectra, we trace the chemical contribution of the rare earth elements (REE)
from various production sites, finding a preference for metal-poor low-mass AGB
stars of 1.5Mo in CEMP-s stars, while CEMP-r/s stars may indicate a more
massive AGB contribution (2-5Mo). A contribution from the r-process - possibly
from neutron star mergers (NSM), is also detectable in the REE abundances,
especially in the CEMP-r/s. Combining spectra with Gaia DR2 astrometric data
indicates that all but one star in our sample (and most literature stars)
belong to the Galactic halo. They exhibit a median orbital eccentricity of 0.7,
and are found on both pro- and retrograde orbits. The orbital parameters of
CEMP-no and CEMP4s stars are remarkably similar in the 98 stars we study. A
special CEMP-no star, with very low Sr and Ba content, possesses the most
eccentric orbit among the stars in our sample, passing close to the Galactic
centre. Finally, we propose an improved scheme to sub-classify the CEMP stars,
making use of the Sr$/$Ba ratio, which can also be used to separate very
metal-poor stars from CEMP stars in 93 stars in the metallicity range
$-4.2<$[Fe/H]$<-2$. The Sr/Ba ratio can also be used for distinguishing
CEMP-s,-r/s and -no stars. The Sr/Ba ratio is also a powerful astro-nuclear
indicator, as AGB stars exhibit very different Sr/Ba ratios, compared to fast
rotating massive stars and NSM, and it is fairly unbiased by NLTE and 3D
corrections.(abridged)
