The flavor structure of the Standard Model (SM), as dictated by the Cabbibo-Kobayashi-Maskawa (CKM) matrix, is far from generic. Probing the elements of the CKM matrix is thus important, not only as tests of the SM but also as probes of new physics beyond it. In part of my work, I look at various phenomena in the realm of flavor physics towards this goal. I focus on the study of the decay of neutral kaons to a dimuon pair. Due to long-distance effects, the decay of the short-lived neutral kaon, $K_S$, to two muons was initially thought to be theoretically unclean. I show that time-dependence measurements of the decay rate are theoretically very clean and can still provide meaningful checks of the Standard Model and look for new physics. The rest of my work is dedicated to the study of neutrinos. Neutrinos are the lightest particles in the Standard Model and they interact very weakly with ordinary matter, making their detection difficult. In my work, I study how an exchange of two neutrinos between two objects can mediate a long ranged force between them, thereby potentially allowing us to probe their properties indirectly. This two-neutrino exchange force, which is a quantum effect, can be treated in the non-relativistic limit as a classical addition to the Coulomb potential. Although this force is weak and below experimental sensitivity levels today, I study how in certain situations it can be enhanced and potentially observed.