We present an experimental study for polycrystalline samples of the diluted magnetic semiconductor Mn(x)Ga(1-x)N (x<0.04) in order to address some of the existing controversial issues. Different techniques were used to characterize the electronic, magnetic, and structural properties of the samples, and inelastic neutron scattering was employed to determine the magnetic excitations associated with Mn monomers and dimers. Our main conclusions are as follows: (i) The valence of the Mn ions is 2+. (ii) The Mn(2+) ions experience a substantial single-ion axial anisotropy with parameter D=0.027(3) meV. (iii) Nearest-neighbor Mn(2+) ions are coupled antiferromagnetically. The exchange parameter J= 0.140(7) meV is independent of the Mn content x, i.e., there is no evidence for hole-induced modifications of J towards a potentially high Curie temperature postulated in the literature.