We study via numerical N-body/smoothed particle hydrodynamics chemistry simulations the effects of primordial non-Gaussianities on the formation of the first stars and galaxies, and investigate the impact of supernova feedback in cosmologies with different fNL. Density distributions are biased to higher values, so star formation and the consequent feedback processes take place earlier in high-fNL models and later in low-fNL ones. Mechanical feedback is responsible for shocking and evacuating the gas from star-forming sites earlier in the highly non-Gaussian cases because of the larger bias at high densities. Chemical feedback translates into high-redshift metal filling factors that are larger by some orders of magnitude for larger fNL, but that converge within one Gyr, for both Population III and Population II-I stellar regimes. The efficient enrichment process, though, leads to metallicities >rsim 10-2 Z⊙ by redshift ˜9, almost independently from fNL. The impact of non-Gaussianities on the formation of dark-matter haloes at high redshift is directly reflected in the properties of the gas in these haloes, as models with larger fNL show more concentrated gas profiles at early times. Non-Gaussian signatures in the gas behaviour are lost after the first feedback takes place and introduces a significant degree of turbulence and chaotic motions. Despite this, our results support the idea that non-Gaussianities can be imprinted in the gaseous and stellar features of primordial structures in the high-redshift Universe.