Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) and other rare-event physics searches, like dark matter detection, have been especially furthered by increasing sensitivity to low-energy particle interactions. Experiments using multiple detector technologies have sought CE$\nu$NS at the most intense terrestrial sources of neutrinos: spallation facilities and nuclear reactors. This thesis reports on the feasibility of using cryogenic pure CsI as an improved next-generation CE$\nu$NS target at the up-and-coming European Spallation Source. Calibrations and simulations presented here predict an increase by a factor of at least $\sim33$ in the rate of observable neutrino-induced events per unit mass, compared to past use of room-temperature CsI[Na]. Also reported is the first measurement of CE$\nu$NS from antineutrinos at the Dresden Generating Station, a power nuclear reactor, employing a large-mass semiconducting germanium diode dubbed NCC-1701. In each section on detecting these neutrino couplings, the importance of understanding device response to low-energy nuclear recoils is highlighted. Finally, finding synergy for tools developed to extricate sub-keV CE$\nu$NS signals, a search for the exotic mode of muon decay $\mu^+ \xrightarrow{} e^+X$ was performed. New sensitivity limits in previously untouched parameter space for a massive boson dark matter candidate of cosmological interest are presented.