If you're really concerned that the system isn't bled correctly, just release the swaybar link and manually work the valve lever all the way up and down. Just be very careful, as you'll be raising and lowering the car to full height and full drop as you do this, and the action is very fast. A few times will guarantee that the struts are properly charged. Best done on a lift or ramps, and allow plenty of safety clearance as the car moves up and down.

The pump operates continuously. When the valve is in the mid-laden position, the flow is routed back around to the reservoir.

When I flush these systems, I suction oil out of the reservoir while running the motor. Work the suspension as described to drop the car to it's lowest postion, suction anything that comes back to the reservoir. Then refill the reservoir and work the suspension through it's travel as described. Suction out as before. Finally fill, work the suspension up and down and check the level. Shouldn't need to be done all that often, unless you have leaky struts.

Finally, as long as the struts don't have major leaks, they have nothing whatsoever to do with ride quality. That's controlled by the spheres, which either work or not. If they've lost some or all of the nitrogen charge, no amount of bleeding can restore them.