I need to obtain and plot electron velocity of the 2DEG in cm/s for different gate and drain biases. In the cutline options I couldn't find anything as electron velocity. I only found electron mobility.
You can extract electron density along the gate length. Then divide current by the sheet electron density. This of course assumes that velocity along each cut line normal to the gate is constant, which should be ok given inversion layer in only a few nanometers thick.