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In this study, we investigate the impact of Weakly Interacting Massive Particles (WIMPs) dark matter (DM) on $C-Λ$ universal relations, GW170817 posterior and radial oscillations of neutron stars (NSs) by considering the interactions of uniformly trapped neutralinos as a DM candidate with the hadronic matter through the exchange of the Higgs boson within the framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The hadronic equation of state (EOS) is modeled using the relativistic mean-field (RMF) formalism with IOPB-I, G3, and QMC-RMF series parameter sets. Presence of DM softens the EOS at both the background and the perturbation levels that implies a small shift to the left in the posterior accompanied by a much larger jump in the left of the mass-radius curves with increasing DM mass. It is observed that EOSs with DM also satisfy the $C-Λ$ universality relations among their-selves but get slightly shifted to the right in comparison to that without considering DM. Additionally, we find that the inclusion of DM allows the mass-radius ($M-R$) curves to remain consistent with observational constraints for HESS J1731-347, indicating the possibility of classifying it as a dark matter-admixed neutron star (DMANS). Moreover, we explore the impact of DM on the radial oscillations of pulsating stars and investigate the stability of NSs. The results demonstrate a positive correlation between the mass of DM and the frequencies of radial oscillation modes.