We have investigated the spin dynamics of a high-mobility two-dimensional electron system (2DES) in a GaAs-Al0.3Ga0.7As single quantum well by time-resolved Faraday rotation in dependence on the initial degree of spin polarization, P, of the 2DES. From P similar to 0 to P similar to 30%, we observe an increase of the spin dephasing time, T-2*, by an order of magnitude, from about 20 ps to 200 ps, in good agreement with theoretical predictions by Weng and Wu [Phys. Rev. B 68, 075312 (2003)]. Furthermore, also the electron g factor is found to decrease for increasing P. Fully microscopic calculations reproduce the most salient features of the experiments, i.e., a dramatic decrease of spin dephasing and a moderate decrease of the electron g factor with increasing P. We show that both results are determined dominantly by the Hartree-Fock contribution of the Coulomb interaction.