We have used large-scale first-principles calculations based on density functional theory to investigate the structure, energetics, electronic, and magnetic structures of Fe-n-doped C-60 monolayers supported by h-BN monolayer-covered Ni(111) surfaces. A systematic study of n-dependent physical properties has been performed (n=1-4,15). Binding energies on Fe atoms to the Fen-1-C-60 complex have been calculated for n=1-4 after a thorough configuration search and structural optimization. The binding energy, electron charge transfer (from Fe-n to C-60), and magnetic moment all increase monotonically as functions of n. The electron charge transfer, ranging from similar to 1e(-) to 5e(-), is from the spin minority population. This leads to a situation in which the net spin of the C-60 molecule aligns with the spin minority and the magnetic moment in C-60 is opposite to the total magnetic moment of the system. For n=2, a competing antiferromagnetic state has been found. In this state, the net spin of the system as well as the C-60 is zero. Density of states and projected density of states analysis indicate that the system becomes metallic upon metal doping regardless its magnetic state. In addition, we have also performed calculations with the Hubbard U term (DFT+U) for two systems, n=4 and 15, to investigate possible gap opening near the Fermi surface.