We theoretically investigate photoinduced phenomena induced by time-periodic driving fields in two-dimensional electron gases under perpendicular magnetic fields with Rashba spin-orbit coupling. Using perturbation theory, we provide analytical results for the Floquet-Landau energy spectrum appearing due to THz radiation. By employing the resulting photomodulated states, we compute the dynamical evolution of the spin polarization function for an initially prepared coherent state. We find that the interplay of the magnetic field, Rashba spin-orbit interaction, and THz radiation can lead to nontrivial beating patterns in the spin polarization. The dynamics also induces fractional revivals in the autocorrelation function due to interference of the photomodulated quantum states. We calculate the transverse photoassisted conductivity in the linear response regime using Kubo formalism and analyze the impact of the radiation field and Rashba spin-orbit interaction. In the static limit we find that our results reduce to well-known expressions of the conductivity in nonrelativistic and quasirelativistic (topological insulator surfaces) two-dimensional electron gas thoroughly described in the literature. We discuss the possible experimental detection of our theoretical prediction and their relevance for spin-orbit physics at high magnetic fields.