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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.