We have studied spin dephasing and spin diffusion in a high-mobility two-dimensional electron system, embedded in a GaAs/AlGaAs quantum well grown in the [110] direction, by a two-beam Hanle experiment. For very low excitation density, we observe spin lifetimes of more than 16 ns, which rapidly decrease as the pump intensity is increased. Two mechanisms contribute to this decrease: The optical excitation produces holes, which lead to a decay of electron spin via the Bir-Aronov-Pikus mechanism and recombination with spin-polarized electrons. By scanning the distance between the pump and probe beams, we observe the diffusion of spin-polarized electrons over more than 20 mu m. For high pump intensity, the spin polarization in a distance of several micrometers from the pump beam is larger than at the pump spot, due to the reduced influence of photogenerated holes.