Pressure Distribution Pattern around Wing
Last question first.  Yes, air does try to "rush" from high to low pressure, but the movement of the wing creates a condition where the net movement of the air relative to the wing will be downwards and backwards, and lower pressure remains above the wing. This is why airspeed is so important.

Understanding the arrows in the diagrams is a bit like reading music or another language.  They are simply pointing from lower to higher pressures.  Isobars on the weather map show the same thing as pressure gradients.

Also important is to know that you are looking at a fully symmetrical airfoil.  There will be equally opposing lower pressure areas top and bottom at 0 angle of attack.  This is why many airfoils have a flat or even concave bottom to help create higher pressure underneath the wing.  But even a fully symmetrical airfoil will have a pressure differential as AoA increases.