Ternary III-nitride alloys have enabled the design of various devices ranging from optoelectronics to power electronics due to their tunable band gap. BxGa1-xN is a wide band gap semiconductor with applications in detecting devices, power electronics and light-emitting diodes. The band gap can be modulated by changing the Boron concentration. It can be grown by metal-organic chemical vapor deposition as a mixed thin film of wurtzite and zincblende structures. In this work, we investigate the structural and electronic properties of BxGa1-xN (x<0.2) by first-principles calculations for both the wurtzite and zincblende phases. The formation energies of Si and Mg impurities and of a Ga vacancy are also calculated. We find that the wurtzite structure is favored over the zincblende structure. Furthermore, the Si and Mg impurities have relatively low formation energies in their neutral state, which indicates compatibility with BxGa1-xN, while a Ga vacancy has very high formation energy, hence being less likely to form spontaneously. Moreover, in the charged states, the formation energy of Mg is reasonably low for most values of the Fermi level, while the formation energy of Si depends linearly on the Fermi level, indicating challenges in achieving n-type conductivity. For a Ga vacancy in a triple acceptor state, the formation energy is reasonably low close to the conduction band, therefore, Ga vacancies interfere with n-type conductivity.