Dipolar gases like erbium and dysprosium have a dense spectrum of resonant loss features associated with their strong anisotropic interaction potential. These resonances display various behaviours with density and temperature, implying diverse microscopic properties. Here, we quantitatively investigate the low-field ($B < 6\,\text{G}$) loss features in ultracold thermal samples of $^{162}$Dy, revealing two- and three-body dominated loss processes. We investigate their temperature dependence and detect a feature compatible with a $d$-wave Fano-Feshbach resonance, which has not been observed before. We also analyse the expansion of the dipolar Bose-Einstein condensate as a function of the magnetic field and interpret the changes in size close to the resonances with a variation in the scattering length.