There is no such thing as "pressure arrow"
Pressure is a scalar quantity, i.e. a magnitude with no direction (NASA).
I believe the points you've raised deserve some attention. @Sanchises is right in that that's just a simplification, but it helps to understand what the author of the image is referring to.
Your image was adapted by Georgia State University from a book by Charles N. Eastlake where he talks about "surface pressure distribution" – even the original image caption reads, "Surface pressure." However, the adapted image says, "Pressure profile around airfoil", which is not as clear as the original caption:
[...] it is also clear that the surface pressure distribution will vary along the chord length of the airfoil, as illustrated in Fig. 3. [emphasis added]
— Eastlake, Charles N. "An aerodynamicist's view of Lift, Bernoulli, and Newton." The Physics Teacher 40.3 (2002): 166-173. (PDF)
So, what are those arrows?
The arrows show the positive direction to/from the datum, and the arrow lengths are the magnitudes near the surface. (The datum of free-stream pressure being the envelope drawn around the airfoil.)
On the upper side the arrows point up towards that datum, meaning whatever is below that datum near the surface is a lower pressure. Similarly, on the lower side the arrows are above the datum, i.e. higher pressure. That drawing is nothing but trying to merge actual pressure distribution graphs (example below) with the shape of an airfoil as a means of explanation.
— Allen, H. Julian. "A simplified method for the calculation of airfoil pressure distribution." (1939).
(Click image to view)
Actual force direction
Zoom in on air molecules, and they exert their pressure everywhere, unless they're right at a surface, in that case the force (pressure times the immediate area) felt by the surface will be down and normal (perpendicular) to the surface, as illustrated by NASA:
— https://www.grc.nasa.gov/www/k-12/airplane/presar.html (I know, the force arrows above do not show the magnitude, but at least the direction is right.)
Given the magnitude of pressure difference on the upper side, lift is primarily achieved by reducing the down-pushing force on the upper side.