Characterizing the physical and chemical properties of forming massive stars at the spatial resolution of individual high-mass cores lies at the heart of current star formation research. We use sub-arcsecond resolution (~0.4arcsec) observations with the NOrthern Extended Millimeter Array at 1.37mm to study the dust emission and molecular gas of 18 high-mass star-forming regions. With distances in the range of 0.7-5.5kpc this corresponds to spatial scales down to 300-2300au that are resolved by our observations. We combine the derived physical and chemical properties of individual cores in these regions to estimate their ages. The temperature structure of these regions are determined by fitting H_2_CO and CH_3_CN line emission. The density profiles are inferred from the 1.37mm continuum visibilities. The column densities of 11 different species are determined by fitting the emission lines with XCLASS. Within the 18 observed regions, we identify 22 individual cores with associated 1.37mm 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 on the order of several 1000au. Comparing these results with values of p derived in the literature suggest that the density profiles remain unchanged from clump to core scales. The column densities relative to N(C18O) between pairs of dense gas tracers show tight correlations. We apply the physical-chemical model MUlti Stage ChemicaL codE (MUSCLE) to the derived column densities of each core and find a mean chemical age of ~60000yrs and an age spread of 20000-100000yrs. With this paper we release all data products of the CORE project available at https://www.mpia.de/core. The CORE sample reveals well constrained density and temperature power-law distributions. Furthermore, we characterize a large variety in molecular richness that can be explained by an age spread confirmed by our physical-chemical modeling. The hot molecular cores show the most 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 again.