fuel filters don't always need to be 100% full and rarely are. How they are positioned has a bearing on this but again, I've owned lots of outboards and rarely is the filter ever 100% full. Fuel bulbs can go soft after the engine starts because fuel is being sucked through them, So two out of two symptoms don't point to the source of the problem. Lack of fuel pressure (such as a weak or bad pump) may be. Try a different portable tank to eliminate the current tank as the problem. Do the cheap stuff first -- like check the plugs, spark on all cylinders, spay a fuel oil mix into the carbs and see if it stays running. If so you confirmed a fuel issue. If not, look elsewhere.