The standard model of particle physics (SM) is a theoretical framework that describes fundamental interactions and constituents of matter. Although very successful in predicting phenomena, in recent years experiments worldwide have reported tensions arising from anomalies observed in the decays of B mesons and in properties of leptons. Most of these tensions strongly point towards new interactions which treat, unlike the SM, leptons of different generations or flavors differently. Such kind of interactions are said to violate lepton flavor universality (LFUV) and might also be the link between ordinary and dark matter (DM). I will discuss an approach to the solution of this problem based on the analysis of the data collected by the Belle II detector at the Super-KEKB, the world's brightest particle accelerator. Three unique searches and some of their by-products will be presented: a search for DM in Z' decays, a search for LFUV in leptonic tau decays and a search for lepton flavor violating (LFV) decays of Y resonances. The three searches are all characterized by final states containing leptons and missing energy that can therefore be analyzed by the same cutting-edge techniques, based on advanced algorithms of machine learning and deep learning that allow to efficiently identify the signals and reject background. Thanks to a new effective field theory approach, these searches will probe additional scenarios of new physics, even beyond the observed anomalies, significantly complementing other searches and experiments.