We present an investigation of electron cyclotron resonance plasma etching induced damage of the 2-dimensional electron gas (2DEG) in GaAs/AlGaAs heterostructures using low temperature photoluminescence (PL), electron paramagnetic resonance (EPR) and the Shubnikov-de Haas (SdH) effect. Dry etching of half of the 20 nm top layer of GaAs results in a decrease of the single-particle relaxation time by 20 - 50%, while the concentration of a surface-related paramagnetic defect increases by about one order of magnitude. At the same time, the PL intensity decreases by a factor of 5 - 10. Plasma hydrogenation experiments, annealing and wet etching experiments have been carried out, and the different characterization results are related to each other. We find that passivation in a hydrogen plasma, which leads to a strong increase of the PL intensity of etched as well as unetched samples, causes damage to the transport properties of the 2DEG. The defect concentration is not related in a simple way to the changes of optical and transport properties.