Simulations of the chemical enrichment histories of ten Local Group (LG) dwarf galaxies are presented, employing empirically-derived star formation histories (SFHs), a rich network of isotopic and elemental nucleosynthetic yields, and a range of prescriptions for supernova (SN)-driven outflows. Our main conclusions are that (i) neutron-capture element patterns (particularly that of Ba/Y) suggest a strong contribution from low- and intermediate-mass stars (LIMS), (ii) neutron star mergers may play a relatively larger role in the nucleosynthesis of dwarfs, (iii) SN feedback alone can explain the observed gas fraction in dwarf irregulars (dIrrs), but dwarf spheroidals (dSphs) require almost all their gas to be removed via ram pressure and/or tidal stripping, (iv) the predicted heavy Mg isotope enhancements in the interstellar medium (ISM) of dwarfs may provide an alternate solution to claims of a varying fine structure (v) the gas lost from dwarfs have O,Si/C abundances in broad agreement with intergalactic medium abundances at redshifts 2<z<4, and (vi) the chemical properties of dSphs are well-matched by preventing galactic winds from re-accreting, whilst those of dIrrs are better-matched by incorporating metallicity-dependent cooling and re-accretion of hot winds. Finally, doubts are cast upon a claimed association between LG dSph UMaII and HVC Complex A.