  The intracluster medium (ICM) is a multi-phase environment, dynamically
regulated by Active Galactic Nuclei (AGN), the motions of galaxies through it,
and mergers with other clusters. AGN as a central heating source are key to
preventing runaway cooling flows, but their role in heating cores in a
cosmological context is still poorly understood. The activity of the AGN is
strongly linked to star formation, especially in the Brightest Cluster Galaxy
(BCG), likely because both rely on cold phase gas. A self-consistent model for
AGN and star formation in galaxy clusters thus requires cosmological context,
higher resolution, and a careful modeling of cooling and heating balance. In
this paper, we use the high-resolution hydrodynamical cosmological simulation
of the RomulusC galaxy cluster to study in detail the role of AGN and a major,
head-on merger in shaping the cluster core. The unprecedented resolution of the
RomulusC simulation captures the multiphase structure of the ICM. The realistic
large-scale outflows launched by very small-scale thermal injections, the
improved modeling of turbulent diffusion and mixing, and the particle nature of
the simulation allow us to carefully separate different heating channels. We
show that AGN activity, while efficient at regulating star formation, is
incapable of destroying a CC. Instead, that process is facilitated by a
head-on, 1:8 mass ratio merger. The merger generates bulk and turbulent
motions, which in turn mix high entropy gas generated by AGN and merger driven
shocks, turbulent dissipation and sloshing of the ICM by infalling
substructures. While central cooling times remain shorter than the Hubble time,
restoring a CC is made more difficult by the reduced precipitation rates at
larger radii, emphasizing that the AGN-ICM connection is truly a multi-scale
problem.
