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Undisturbed galaxy clusters are characterized by a massive and large elliptical galaxy at their center, i.e. the Brightest Cluster Galaxy (BCG). How these central galaxies form is still debated. According to most models, a typical epoch for their assembly is z~1-2. We have performed a detailed multi-wavelength analysis of the core of XDCPJ0044.0-2033 (XDCP0044), one of the most massive and densest galaxy clusters currently known at redshift z~1.6, whose central galaxy population shows high star formation compared to lower-z clusters and an X-ray AGN located close to its center. SINFONI J-, H- and KMOS YJ-, H- bands spectroscopic data have been analyzed, together with deep archival HST photometric data in F105W, F140W, and F160W bands, Chandra X-ray, radio JVLA data at 1-2 GHz, and ALMA band-6 observations. In the central region of the cluster (~70x70 kpc^2), 2 systems of interacting galaxies have been identified and studied (Complex A and B), with a total of 7 confirmed cluster members. These galaxies show perturbed morphologies and 3 of them show signs of AGN activity. In particular, 2 type-1 AGN with typical broad lines have been found at the center of each complex (both of them X-ray obscured and highly accreting; Eddington ratio ~0.5), while a type-2 AGN has been discovered in Complex A. The AGN at the center of Complex B is also detected in X-ray while the other 2 are spatially related to radio emission. The 3 AGN provide one of the closest AGN triple at z>1 revealed so far with a minimum(maximum) projected distance of ~10(40) kpc. The observation of high star formation, merger signatures and nuclear activity in the core of XDCP0044 suggests that all these processes are key ingredients in shaping the nascent BCG. According to our data, XDCP0044 could form a typical massive galaxy of 10^12 Msun, hosting a Black Hole of 2x10^8-10^9 Msun, in a time scale of the order of ~2.5 Gyrs., 15 pages, 10 figures, 5 tables. Accepted to MNRAS in 2020 August 14