<p>In this study, we explored the electronic properties of a two-dimensional graphene lattice in the presence of an external magnetic field, Rashba spin-orbit coupling. Our focus was on investigating the energy-dependent behavior of the electronic heat capacity and paramagnetic spin susceptibility in response to changing factors. Employing the Green’s function approach, we successfully determined the energy dependence of the electronic heat capacity and paramagnetic susceptibility using the Kane-Mele model including Zeeman term. Notably, at low energies, the electronic heat capacity almost shows an exponential behavior, while the paramagnetic susceptibility drastically decreases at very low temperatures for some amounts of Rashba spin-orbit coupling. Furthermore, we conducted a detailed investigation of the energy-dependent paramagnetic susceptibility and electronic heat capacity of a graphene monolayer, considering the influences of Rashba spin-orbit coupling and magnetic field factors. Our investigation of the density of states in the presence of SOC suggests that semimetal-to-metal phase transitions occur at zero magnetic field. While we have found a phase transition from metal-to-semiconductor under the influence of Rashba spin-orbit coupling in the presence of a magnetic field. We found that these alterations, along with the splitting of levels under different conditions, led to changes in the material’s electrical properties. We have also studied the optical absorption of graphene monolayer under influences of Rashba spin-orbit coupling and magnetic field factors.</p>