We present 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 density functional+dynamical mean-field theory approach. In particular, we explore the impact of epitaxial compressive strain that experience (Nd,Sr)NiO2 films on the electronic properties, magnetic correlations, and exchange couplings. Our results reveal the crucial importance of orbital-dependent correlation effects in the Ni 3d shell of Sr-doped NdNiO2. 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 Néel ( 111) antiferromagnetic (AFM) order, while for x > 0.2 the C-type (110) AFM sets in the unstrained (Nd,Sr)NiO2, with a highly frustrated region at x 0.2, all within DFT+DMFT at T = 290 K. Our results for the Néel 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. Our results for magnetic couplings demonstrate an unanticipated frustration of the Ni 3d magnetic moments, which suppresses magnetic order near Sr x = 0.2. We find that the effect of frustration is maximal for Sr doping x 0.1 − 0.2 that nearly corresponds to the experimentally observed doping value. 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 suppresses the static C-type (110) ordering in (Nd,Sr)NiO2 for Sr x > 0.2. Moreover, the in-plane strain affects the character of the Fermi surface of Sr-doped NdNiO2 near the Brillouin zone A point, adjusting the crossover from electron-to hole-like behavior at high Sr x. The electronic structure and magnetic correlations of (Nd,Sr)NiO2 reveal an anomalous sensitivity upon a change of the crystal structure parameters.