  Using density functional based LDA+U method and linear-response theory, we
study the magnetic exchange interactions of the superconductor
Nd{1-x}Sr{x}NiO2. Our calculated nearest-neighbor exchange constant J1=82 meV
is large, weakly affected by doping and is only slightly smaller than that
found in the sister compound CaCuO2. We however find that the hole doping
significantly enhances the inter--layer exchange coupling as it affects the
magnetic moment of the Ni-3d{3z2-r2} orbital. This can be understood in terms
of small hybridization of Ni-3d{3z2-r2} within the NiO2 plane which results in
a flat band near the Fermi level, and its large overlap along z direction. We
also demonstrate that the Nd-5d states appearing at the Fermi level, do not
affect the magnetic exchange interactions, and thus may not participate in the
superconductivity of this compound. Whereas many previous works emphasize the
importance of the Ni-3d{x2-y2} and Nd-5d orbitals, we instead analyze the
solution of Ni-3d{x2-y2}/Ni-3d{3z2-r2} minimal model using Dynamical Mean Field
Theory. It reveals an underlying Mott insulating state which, depending on
precise values of the intra--atomic Hund's coupling less or larger than 0.83
eV, selects upon doping either S=0 or S=1 two--hole states at low energies
leading to very different quasiparticle band structures. We propose that trends
upon doping in spin excitational spectrum and quasiparticle density of state
can be a way to probe Ni 3d8 configuration.
