1. All of it. A difference in air pressure is just an abstraction for talking about forces on air particles. The description of what's going on with the screwdriver would be equivalent physically and much more intuitive if air pressure wasn't mentioned at all.
What's going on is the curved back pulls air around it, which deflects it downward, and that downward force on the air implies an upward force on the screwdriver. With the sharp edge back, this detaches the air flow instead, meaning there's much less deflection, and thus less force.
The air-deflection model is a much better intuition pump than the air pressure model. I think the historical dominance of the air pressure model is because it's easier to measure - just stick some air pressure gauges on surfaces, and you can calculate what that means for lift.
I guess it differs between people, what is easier to grasp :) . Pressure of air makes a real physical force (actually, pressure is defined as that total force divided by area). At the same time deflection downward, which implies an upward force, is correct but doesn't show the mechanism how actually that implied force is born. It is born out of the difference of pressure between top of the screwdriver and the bottom - at the bottom you have more or less undisturbed ambient pressure, at the top the flow reduces the pressure.
What was interesting to me is Ben's experiment with long enough cone which failed to get lift. Shouldn't be so, I think. The problem could be that his air jet is relatively narrow - so with a long cone, which makes an angle with the stream not the whole cone gets flown over, and not the whole area is under the reduced pressure. It would be very interesting to see if a wider air jet would still fail to lift the long tapered cone.
The largest forces here are gravity and the air directly hitting at the screwdriver. Other forces (Coanda effect) stabilize the screwdriver. Different air hose angles would send the screwdriver flying or let it drop.
To rephrase the question, how much of the lift is generated by high-pressure air below the screwdriver, and how much is generated by low-pressure air above?
Pressure is relative, and it is this pressure difference that causes the lifting force. So what is "high pressure" relative to the top of the screwdriver is "low pressure" relative to the bottom of it (and the atmosphere.)
It depends what type of pressure you mean; the stream of air has a high dynamic pressure, but its static pressure is the same as atmospheric.[1] In any case, the air is not directed at the bottom of the screwdriver but at its side. It follows the surface (Coandă effect[2]) and then creates a region of low (static) pressure near the tip when it separates. This is lower than the atmospheric pressure at the bottom; thus there is lift.
The air at the nozzle mouth is at 100 psi, and there is a high pressure region around the nozzle. It is not correct to say that the static pressure is the same as atmospheric.
It is correct to say that the static pressure is atmospheric pressure. Inside the nozzle the pressure was 100psi when stationary, the static pressure was traded for dynamic pressure when it exited the confinement of the pressure vessel.
1. How much of the lift is caused just by the air pushing up?
2. The turbulence caused by a square back is (I think) why rear windows should be closed in a pickup - prevents the exhaust from coming in.