  We present the Rhapsody-C simulations that extend the Rhapsody-G suite of
massive galaxy clusters at the $M_{\rm vir}\sim10^{15}\thinspace{\rm
M}_{\odot}$ scale with cosmological magneto-hydrodynamic zoom-in simulations
that include anisotropic thermal conduction, modified supermassive black hole
(SMBH) feedback, new SMBH seeding and SMBH orbital decay model. These modelling
improvements have a dramatic effect on the SMBH growth, star formation and gas
depletion in the proto-clusters. We explore the parameter space of the models
and report their effect on both star formation and the thermodynamics of the
intra-cluster medium (ICM) as observed in X-ray and SZ observations. We report
that the star formation in proto-clusters is strongly impacted by the choice of
the SMBH seeding as well as the orbital decay of SMBHs. Feedback from AGNs is
substantially boosted by the SMBH decay, its time evolution and impact range
differ noticeably depending on the AGN energy injection scheme used. Compared
to a mass-weighted injection whose energy remains confined close to the central
SMBHs, a volume-weighted thermal energy deposition allows to heat the ICM out
to large radii which severely quenches the star formation in proto-clusters. By
flattening out temperature gradients in the ICM, anisotropic thermal conduction
can reduce star formation early on but weakens and delays the AGN activity.
Despite the dissimilarities found in the stellar and gaseous content of our
haloes, the cluster scaling relations we report are surprisingly insensitive to
the subresolution models used and are in good agreement with recent
observational and numerical studies.
