We study a suite of extremely high-resolution cosmological Feedback in Realistic Environments simulations of dwarf galaxies (M_(halo) ≲ 10¹⁰ M⊙), run to z = 0 with 30M⊙ resolution, sufficient (for the first time) to resolve the internal structure of individual supernovae remnants within the cooling radius. Every halo with M_(halo) ≳ 10_(8.6) M⊙ is populated by a resolved stellar galaxy, suggesting very low-mass dwarfs may be ubiquitous in the field. Our ultra-faint dwarfs (UFDs; M∗ 10⁵ M⊙) continue forming stars to z 10⁻⁴ to form a dark matter core > 200pc, while lower mass UFDs exhibit cusps down to ≲ 100pc, as expected from energetic arguments. Our dwarfs with M∗ > 10₄ M⊙ have half-mass radii (R_(1/2)) in agreement with Local Group (LG) dwarfs (dynamical mass versus R_(1/2) and stellar rotation also resemble observations). The lowest mass UFDs are below surface brightness limits of current surveys but are potentially visible in next-generation surveys (e.g. LSST). The stellar metallicities are lower than in LG dwarfs; this may reflect pre-enrichment of the LG by the massive hosts or Pop-III stars. Consistency with lower resolution studies implies that our simulations are numerically robust (for a given physical model)