An optical pumping technique was used to enhance and localize nuclear magnetic resonance (NMR) signals from an n-doped GaAs/Al0.1Ga0.9As multiple quantum well structure, permitting direct radio-frequency measurements of gallium-71 NMR spectra and nuclear spin-lattice relaxation rates (1/T1) as functions of temperature (1.6 K < T < 4.2 K) and the Landau level filling factor (0.66 < v < 1.76). The measurements reveal effects of electron-electron interactions on the energy levels and spin states of the two-dimensional electron system confined in the GaAs wells. Minima in 1/T1 at v approximately 1 and v approximately 2/3 indicate energy gaps for electronic excitations in both integer and fractional quantum Hall states. Rapid, temperature-independent relaxation at intermediate v values indicates a manifold of low-lying electronic states with mixed spin polarizations.