How does experienced pressure vary with airspeed?
1) Pressure is simply a force divided by an area, so yes: The dynamic pressure experienced by a forward-facing surface will, in an incompressible flow, vary with the square of the speed.

2) The dynamic pressure increases dramatically as one approaches the speed of sound, once going faster than mach one the pressure will begin to decrease. The trans-sonic phase (around mach one) is difficult to describe and can depend on the airflow around the body - but in many cases it can be quite stable.

-edit-
For the second question here's a couple of links that can provide more information:


Transonic flow around a rocket
NASA history of transonic research