GaN single crystals with size of up to 2.4 mm were grown from complex liquid alkali flux with Na, Li, Ga and C as main components. The resulting GaN crystals were characterized by several techniques: powder X-Ray diffraction to evaluate crystalline phases, scanning electron microscopy (SEM) to determine the morphology and size of the crystallites, and photoluminescence and cathodoluminescence to evaluate the quality of the crystals. Low-temperature and roomtemperature photoluminescence of the near-edge-band transitions at 3.4-3.5 eV, DAP transitions at 3.0-3.1 eV, and yellow band transitions at 2.2-2.3 eV in GaN samples were observed. It is established that yellow PL band centered at 540 nm is related to the nitrogen vacancies or (V_Ga-O_N) complexes. The NIR PL band with maximum at 780 nm was observed in the PL spectra of GaN samples and is due to structural defects and oxygen impurity. The positive influence of carbon doping on GaN growth was demonstrated and discussed. It was found that KCN doping of alkali flux lead to the poor GaN crystals quality with weakly photoluminescence emission in the near-edgeband region. Our results address the radiative recombination processes in GaN, and can be used for optimization of GaN-based optoelectronic devices and nanostructures.