  Motivated by the recent discovery of superconductivity in the infinite-layer
(Sr,Nd)NiO$_2$ films with Sr content $x \simeq0.2$ [Li et al., Nature (London)
\textbf{572}, 624 (2019)], we examine the effects of electron correlations and
Sr-doping on the electronic structure, Fermi surface topology, and magnetic
correlations in (Nd,Sr)NiO$_2$ using a combination of dynamical mean-field
theory of correlated electrons and band-structure methods. Our results reveal a
remarkable orbital selective renormalization of the Ni $3d$ bands, with
$m$*/$m\sim 3$ and 1.3 for the $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals,
respectively, that suggests orbital-dependent localization of the Ni $3d$
states. We find that upon hole doping (Nd,Sr)NiO$_2$ undergoes a Lifshitz
transition of the Fermi surface which is accompanied by a change of magnetic
correlations from the three-dimensional (3D) N\'eel $G$-type (111) to the
quasi-2D $C$-type (110). We show that magnetic interactions in (Nd,Sr)NiO$_2$
demonstrate an unanticipated frustration, which suppresses magnetic order,
implying the importance of in-plane spin fluctuations to explain its
superconductivity. Our results suggest that frustration is maximal for
Sr-doping $x \simeq 0.1$--0.2, which is in agreement with an experimentally
observed doping value Sr $x \simeq 0.2$ of superconducting (Nd,Sr)NiO$_2$.
