We report a theoretical study of the effect of electron-electron interactions and Sr doping on the electronic structure of infinite-layer (Nd,Sr)NiO2 using the DFT+dynamical mean-field theory approach (DFT+DMFT). Here, we explore the effect of lattice strain that experience (Nd,Sr)NiO2 films upon growing on the SrTiO3 substrate on the electronic properties, magnetic correlations, and exchange couplings of (Nd,Sr)NiO2. For both strained and unstrained Sr-doped NdNiO2 our results reveal the crucial importance of orbital-de-pendent correlation effects in the Ni 3d shell. Upon doping with Sr, it undergoes a Lifshitz transition which is accompanied by a reconstruction of magnetic correlations. For Sr x < 0.2 (Nd,Sr)NiO2 adopts the Neel (111) antiferromagnetic (AFM) order, while for x > 0.3 the C-type (110) AFM sets in the unstrained (Nd,Sr) NiO2, with a highly frustrated region at x similar or equal to 0.2, all within DFT+DMFT at T = 290 K. Our results for the Neel AFM at Sr x = 0 suggest that AFM NdNiO2 appears at the verge of a Mott-Hubbard transition, providing a plausible explanation for the experimentally observed weakly insulating behavior of NdNiO2 for Sr x < 0.1. We observe that the Lifshitz transition makes a change of the band structure character from electron- to hole-like with Sr x, in agreement with recent experiments. We conclude that the in-plane strain adjusts a bandwidth of the Ni x(2)-y(2) band, i.e., controls the effect of electron correlations in the Ni x(2)-y(2) orbitals. It leads to a suppression of the static C-type (110) ordering in (Nd,Sr)NiO2 for Sr x > 0.3. Our results for the electronic structure and magnetic correlations of (Nd,Sr)NiO2 reveal an anomalous sensitivity upon a change of the crystal structure parameters. (C) 2021 Elsevier B.V. All rights reserved.