The structural, electronic, and magnetic properties of two-dimensional (2D) GaS are investigated using density functional theory (DFT). After confirming that the pristine 2D GaS is a non-magnetic, indirect band gap semiconductor, we consider N and F as substitutional dopants or adsorbed atoms. Except for N substituting for Ga (NGa), all considered cases are found to possess a magnetic moment. Fluorine, both in its atomic and molecular form, undergoes a highly exothermic reaction with GaS. Its site preference (FS or FGa) as substitutional dopant depends on Ga-rich or S-rich conditions. Both for FGa and F adsorption at the Ga site, a strong F-Ga bond is formed, resulting in broken bonds within the GaS monolayer. As a result, FGa induces p-type conductivity in GaS, whereas FS induces a dispersive, partly occupied impurity band about 0.5 e below the conduction band edge of GaS. Substitutional doping with N at both the S and the Ga site is exothermic when using N atoms, whereas only the more favourable site under the prevailing conditions can be accessed by the less reactive N2 molecules. While NGa induces a deep level occupied by one electron at 0.5 eV above the valence band, non-magnetic NS impurities in sufficiently high concentrations modify the band structure such that a direct transition between N-induced states becomes possible. This effect can be exploited to render monolayer GaS a direct-band gap semiconductor for optoelectronic applications. Moreover, functionalization by N or F adsorption on GaS leads to in-gap states with characteristic transition energies that can be used to tune light absorption and emission. These results suggest that GaS is a good candidate for design and construction of 2D optoelectronic and spintronics devices.