To answer your first question, yes there is a check valve at the bottom of the aluminium tube that runs from the pump to the top of the tank. You will usually not notice a problem with it while running but when it gets stuck open it will have an extremely hard time starting again when there is pressure in the tank. The check valve essentially keeps the tank pressure off of the top of the piston when it tries to restart. What you need to do is get an electrical meter and read the voltage going to the air compressor while it is running. Se how far below 220v it is dropping when it is getting up to pressure. It is very possible the generator cannot keep the voltage up with the load demand.