The density of air varies with pressure and temperature. So, in principle, flow of air is always compressible. No shock waves. Flows with regions of subsonic and supersonic flow. Subsonic flows are characterized by smooth streamlines.
Disturbances can propagate both upstream and downstream.
Velocity over an airfoil increases as the airfoil gets wider. The local velocity exceeds the speed of sound. Shock waves may occur. Expansion waves may be exhibited. Disturbances cannot propagate upstream.