  We use sub-arcsecond resolution ($\sim$0.4$''$) observations with NOEMA at
1.37 mm to study the dust emission and molecular gas of 18 high-mass
star-forming regions. We combine the derived physical and chemical properties
of individual cores in these regions to estimate their ages. The temperature
structure of these regions are determined by fitting H2CO and CH3CN line
emission. The density profiles are inferred from the 1.37 mm continuum
visibilities. The column densities of 11 different species are determined by
fitting the emission lines with XCLASS. Within the 18 observed regions, we
identify 22 individual cores with associated 1.37 mm continuum emission and
with a radially decreasing temperature profile. We find an average temperature
power-law index of q = 0.4$\pm$0.1 and an average density power-law index of p
= 2.0$\pm$0.2 on scales on the order of several 1 000 au. 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 MUSCLE to the derived column densities of
each core and find a mean chemical age of $\sim$60 000 yrs and an age spread of
20 000-100 000 yrs. 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.
