  We investigate various galaxy population properties of the massive X-ray
luminous galaxy cluster XDCP J0044.0-2033 at z=1.58, which constitutes the most
extreme matter density peak at this redshift currently known. We analyze deep
VLT/HAWK-I NIR data in the J- and Ks-bands, complemented by Subaru imaging in i
and V, Spitzer observations at 4.5 micron, and new spectroscopic observations
with VLT/FORS2. We detect a cluster-associated excess population of about 90
galaxies, which follows a centrally peaked, compact NFW galaxy surface density
profile with a concentration of c200~10. Based on the Spitzer 4.5 micron
imaging data, we measure a stellar mass fraction of fstar,500=(3.3+-1.4)%
consistent with local values. The total J- and Ks-band galaxy luminosity
functions of the core region yield characteristic magnitudes J* and Ks*
consistent with expectations from simple z_f=3 burst models. However, a
detailed look at the morphologies and color distributions of the
spectroscopically confirmed members reveals that the most massive galaxies are
undergoing a very active mass assembly epoch through merging processes.
Consequently, the bright end of the cluster red-sequence is not in place, while
at intermediate magnitudes [Ks*,Ks*+1.6] a red-locus population is present,
which is then sharply truncated at magnitudes fainter than Ks*+1.6. The
dominant cluster core population comprises post-quenched galaxies transitioning
towards the red-sequence at intermediate magnitudes, while additionally a
significant blue cloud population of faint star-forming galaxies is present
even in the densest central regions. Our observations lend support to the
scenario in which the dominant effect of the dense z~1.6 cluster environment is
an accelerated mass assembly timescale through merging activity that is
responsible for driving core galaxies across the mass quenching threshold of
log(Mstar/Msun)~10.4.
