We determine atomic structure, electronic structure, formation energies, magnetic properties of native point defects, such as gallium (Ga) and nitrogen (N) vacancies, in bulk and at the nonpolar ($10\overline{1}0$) surface of wurtzite gallium nitride (w-GaN) using first-principles density functional theory (DFT) based calculations. In bulk and at the ($10\overline{1}0$) surface of GaN, N vacancies are significantly more stable than Ga vacancies under both Ga-rich and N-rich conditions. We show that within DFT-local density approximated N vacancies form spontaneously at the ($10\overline{1}0$) surface of GaN when doped to raise the Fermi level up to ≈ 1.0 eV above valence band maximum (VBM) while with valence band edge correction it is 1.79 eV above VBM. We provide experimental evidence for occurrence of N vacancies with electron energy loss spectroscopy measurements, which further hints the N vacancies at surface to the source of auto-doping which may explain high electrical conductivity of GaN nanowall network grown with molecular beam epitaxy.