We present the non-local thermodynamic equilibrium (NLTE) abundances of up to 10 chemical species in a sample of 59 very metal-poor (VMP, -4 <= [Fe/H] less than or similar to -2) stars in seven dwarf spheroidal galaxies (dSphs) and in the Milky Way (MW) halo. Our results are based on high-resolution spectroscopic datasets and homogeneous and accurate atmospheric parameters determined in Paper I. We show that once the NLTE effects are properly taken into account, all massive galaxies in our sample, that is, the MW halo and the classical dSphs Sculptor, Ursa Minor, Sextans, and Fornax, reveal a similar plateau at [alpha/Fe] similar or equal to 0.3 for each of the alpha-process elements: Mg, Ca, and Ti. We put on a firm ground the evidence for a decline in alpha/Fe with increasing metallicity in the Bootes I ultra-faint dwarf galaxy (UFD), that is most probably due to the ejecta of type Ia supernovae. For Na/Fe, Na/Mg, and Al/Mg, the MW halo and all dSphs reveal indistinguishable trends with metallicity, suggesting that the processes of Na and Al synthesis are identical in all systems, independent of their mass. The dichotomy in the [Sr/Ba] versus [Ba/H] diagram is observed in the classical dSphs, similarly to the MW halo, calling for two different nucleosynthesis channels for Sr. We show that Sr in the massive galaxies is well correlated with Mg suggesting a strong link to massive stars and that its origin is essentially independent of Ba, for most of the [Ba/H] range. Our three UFDs, that is Bootes I, UMa II, and Leo IV, are depleted in Sr and Ba relative to Fe and Mg, with very similar ratios of [Sr/Mg] similar or equal to -13 and [Ba/Mg] similar or equal to -1 on the entire range of their Mg abundances. The subsolar Sr/Ba ratios of Bootes I and UMa II indicate a common r-process origin of their neutron-capture elements. Sculptor remains the classical dSph, in which the evidence for inhomogeneous mixing in the early evolution stage, at [Fe/H] < -2, is the strongest.