The present work is devoted to a comprehensive study of dilute (Ga,Mn)N grown by MOVPE, with the target of establishing the correlation between growth parameters, structural and magnetic properties in order to clarify the actual mechanisms responsible for the magnetic response of the considered system. We combine on-line control of the growth process with a variety of standard characterization techniques including AFM, HRXRD, Raman spectroscopy, magneto-optics and SQUID magnetometry, complemented by advanced investigation carried-out by means of synchrotron XRD, XAFS and HRTEM. We demonstrate that dilute (Ga,Mn)N with a Mn cations concentration up to 1% has a paramagnetic behaviour with a pronounced anisotropy of the magnetization with respect to the c axis of the crystal. Moreover, most of the cations are incorporated substitutionally at Ga sites with a charge state of 3+, that can be reduced by doping with Si. Further adjustment of the growth parameters allow us to extend the the dilute incorporation of Mn in GaN up to 3% and to clearly establish a short-range ferromagnetic coupling of the Mn cations spins via superexchange.