Is the angle of attack equal to zero when the plane is on the ground with wings level?
You're right to be confused. The AoA can be almost anything, depending on wind direction. Normally, a wing has some camber so the lift it creates in flight is possible with an AoA of 0°. Normally, the wing is mounted at an incidence of a few degrees so the fuselage remains horizontal in flight. With this incidence and horizontal wind, the AoA at rest is just this incidence angle. But if the aircraft experiences tailwind, the AoA can be near 180°. If heated air below the wing rises up as a thermal, the AoA can be momentarily around 90°. In almost all cases, flow speed is much lower than that required for flight, but there are exceptions.