  Using high-resolution simulations from the FIRE-2 (Feedback In Realistic
Environments) project, we study the effects of discreteness in stellar feedback
processes on the evolution of galaxies and the properties of the interstellar
medium (ISM). We specifically consider the discretization of supernovae (SNe),
including hypernovae (HNe), and sampling the initial mass function (IMF). We
study these processes in cosmological simulations of dwarf galaxies with $z=0$
stellar masses $M_{\ast}\sim 10^{4}-3\times10^{6}\,M_\odot$ (halo masses $\sim
10^{9}-10^{10}\,M_\odot$). We show that the discrete nature of individual SNe
(as opposed to a model in which their energy/momentum deposition is continuous
over time, similar to stellar winds) is crucial in generating a reasonable ISM
structure and galactic winds and in regulating dwarf stellar masses. However,
once SNe are discretized, accounting for the effects of IMF sampling on
continuous mechanisms such as radiative feedback and stellar mass-loss (as
opposed to adopting IMF-averaged rates) has weak effects on galaxy-scale
properties. We also consider the effects of rare HNe events with energies $\sim
10^{53}\,{\rm erg}$. The effects of HNe are similar to the effects of clustered
explosions of SNe -- which are already captured in our default simulation setup
-- and do not quench star formation (provided that the HNe do not dominate the
total SNe energy budget), which suggests that HNe yield products should be
observable in ultra-faint dwarfs today.
