Aims. Current star formation research centers the characterization of the physical and chemical properties of massive stars, which are in the process of formation, at the spatial resolution of individual high-mass cores. Methods. We use sub-arcsecond resolution (~0.$$^{′′}$$4) observations with the NOrthern Extended Millimeter Array at 1.37 mm to study the dust emission and molecular gas of 18 high-mass star-forming regions. With distances in the range of 0.7−5.5 kpc, this corresponds to spatial scales down to 300−2300 au that are resolved by our observations. We combined the derived physical and chemical properties of individual cores in these regions to estimate their ages. The temperature structures of these regions are determined by fitting the H$$_2$$CO and CH$$_3$$CN line emission. The density profiles are inferred from the 1.37 mm continuum visibilities. The column densities of 11 different species are determined by fitting the emission lines with XCLASS. Results. Within the 18 observed regions, we identified 22 individual cores with associated 1.37 mm continuum emission and with a radially decreasing temperature profile. We find an average temperature power-law index of q = 0.4 ± 0.1 and an average density power-law index of p = 2.0 ± 0.2 on scales that are on the order of several 1000 au. Comparing these results with values of p derived from the literature presumes that the density profiles remain unchanged from clump to core scales. The column densities relative to N(C$$^{18}$$O) between pairs of dense gas tracers show tight correlations. We applied the physical-chemical model MUlti Stage ChemicaL codE to the derived column densities of each core and find a mean chemical age of ~60 000 yr and an age spread of 20 000−100 000 yr. With this paper, we release all data products of the CORE project. Conclusions. The CORE sample reveals well-constrained density and temperature power-law distributions. Furthermore, we characterized a large variety in molecular richness that can be explained by an age spread that is then confirmed by our physical-chemical modeling. The hot molecular cores show the greatest number of emission lines, but we also find evolved cores at an evolutionary stage in which most molecules are destroyed and, thus, the spectra appear line-poor once again.