Rechargeable magnesium-ion batteries (MIBs) are a promising alternative to commercial lithium-ion batteries (LIBs). They are safer to handle, environmentally more friendly, and provide a five-time higher volumetric capacity (3832 mAh cm$^{-3}$) than commercialized LIBs. However, the formation of a passivation layer on metallic Mg electrodes is still a major challenge towards their commercialization. Using density functional theory (DFT), the atomistic properties of metallic magnesium, mainly well-selected self-diffusion processes on perfect and imperfect Mg surfaces were investigated to better understand the initial surface growth phenomena. Subsequently, rate constants and activation temperatures of crucial diffusion processes on Mg(0001) and Mg(10$_{overline{1}}$ 1) were determined, providing preliminary insights into the surface kinetics of metallic Mg electrodes. The obtained DFT results provide a data set for parametrizing a force field for metallic Mg or performing kinetic Monte-Carlo simulations.