[Does] all of the low pressure created by the airfoil gets recovered on the rear side of the wing?
Only in inviscid flow. Then we speak of a rear stagnation point.
In reality, viscous effects cause enough energy loss that the static pressure at the trailing edge rises only a bit above its ambient value from the confluence of upper and lower flow and then quickly drops to ambient pressure when you follow the streamline from the trailing edge into the wake. See below for the XFOIL pressure coefficient plot of the HQ-17 airfoil.
If you put a pressure sensor right behind the trailing edge of an airfoil, would the pressure be the same as ambient, higher, lower?
That depends on the direction in which the sensor is pointing. Normally, those sensors are placed in flow direction so they measure the total pressure (sum of static and dynamic pressure). A rake of those is used to measure the pressure distribution over the height of the wake which is a very good way to determine the drag of airfoils. In the wake, total pressure is quite a bit below its freestream value due to the slowing down of flow speed in the boundary layer.
If you point the sensor in a direction orthogonal to flow speed, it should measure static pressure. With attached flow the pressure would be slightly higher than ambient and with separated flow it would drop below ambient pressure.