what is the air value on top of the tank for? Can you add more pressure (air) to the tank... and get more pressure out?

Its used to adjust volume of the bladder inside the tank. Its not for adjusting the water pressure.

The pressure at the top of the tank should be set to 2# BELOW the cut in pressure for the pump. For instance, if the pump cuts on at 30#, then you would set the pressure at the top of the tank to 28#. Do this with the system off and pressure drained to zero.

Once set, don't change it. It is, as Smoothy pointed out, not there to adjust system pressure.