Q: When car starts, it shudders before shutting off

I am seeking assistance regarding fuel problems in my car. My car is having trouble “staying” on after starting. Occasionally I have difficulty getting it to start. When it does turn over, it shudders and then dies; the gas pedal is inoperative; and it acts like it is out of gas. These problems grow worse when the tank is less than ½ full and adding gas to it does help the problem. The gas gauge reads “less” than the amount that is truly in the gas tank. It will stall at intersections, but never stalls while I’m driving. Also, there is air in the fuel line. It also idles rough and this problem also improves when on a full tank of gas. A mechanic cleaned the fuel injectors and then told me it was fine; however, the same problems still exists and the cleaning did nothing of benefit, it seems. What can I do to correct these problems in my car?