  The novel nickelate superconductors of infinite-layer type feature
challenging electronic pecularities in the normal-state phase diagram with
doping. Distinct many-body behavior and different dispersion regimes of the
entangled $\{$Ni-$d_{z^2}$, Ni-$d_{x^2-y^2}$$\}$ orbital sector give rise to
highly rich physics, which is here studied for the case of the NdNiO$_2$
system. An analysis based on advanced realistic dynamical mean-field theory
unveils that the superconducting hole-doped region is the meeting place of a
(self-)doped Mott insulator from the underdoped side, and a bad Hund metal from
the overdoped side. Fermi-level crossing of the Ni-$d_{z^2}$ flat-band ties
both regimes together to form a singular arena for unconventional
superconductivity. We furthermore shed light on the intriguing problem of
elusive magnetism in infinite-layer nickelates. Antiferromagnetic (AFM) order
with small Ni moments is shown to be a vital competitor at low temperature. At
stoichiometry, C-AFM order with ferromagnetic spin-alignment along the $c$-axis
benefits from a conceivable coexistence with Kondo(-lattice) screening.
