We present a fully parallel chemo-dynamical Tree/SPH code, GEAR, which allows to perform high resolution simulations with detailed chemical diagnostics. Starting from the public version of Gadget-2, we included the complex treatment of the baryon physics: gas cooling, star formation law, chemical evolution and supernovae feedback. We qualified the performances of GEAR with the case of dSph galaxies. GEAR conserves the total energy budget of the systems to better than 5% over 14Gyr and proved excellent convergence of the results with numerical resolution. We showed that models of dSphs in a static Euclidean space, where the expansion of the universe is neglected are valid. In addition, we tackled some of the existing open questions in the field, like the stellar mass fraction of dSphs and its link with the predicted dark matter halo mass function, the effect of the supernova feedback, the spatial distribution of the stellar populations, and the origin of the diversity in star formation histories and chemical abundance patterns. Strong supernovae driven winds seem incompatible with the observed metallicities and luminosities. Despite the fact that newly formed stars are preferentially found in the galaxy central parts, turbulent motions in the gas can quickly erase any metallicity gradient. The variety in dSph properties result from a range of total masses as well as from a dispersion in central densities. The latter is also seen in the haloes emerging from a LCDM cosmogony.