it is clear that the overall integrated pressure on the top of the wing is less than the overall pressure at the bottom of a wing in order to produce a net nonzero lift force. Based on the attached figure below (AoA going from small to large), it seems that, for low and medium angles of attack, the pressure both at the top and bottom surfaces of the wing is lower than the free stream atmospheric pressure. The arrows' directions, from what I understand, are pressure gradients pointing toward higher pressure area, correct?
When the angle of attack is sufficiently large, the pressure on the wing's bottom surface is higher than the free stream pressure (positive pressure coefficient)...Is that correct?

Whenever the local pressure is lower than atmospheric pressure, I think air would rush to that area so air would be moving from far above the wing towards the wing top surface (same for bottom wing surface when the pressure coefficient is negative). Is that what happens? 
Thanks.
[![enter image description here][1]][1]

  [1]: https://i.sstatic.net/S8eE0.png