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)
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