Some think they are more problem prone than others and a couple of years ago, the one that started with F in the parts number was failing left and right. Some say it was fixed, but, I am not so sure. There are also a lot of counterfeit Walbros reportedly on the market...but I have seen other brands fail as well. Saw a new DW pump fail recently.
Then, there are problems that occur because the hose in the tank that goes to the pump was not tightened enuf, or was overtightened and cracked the hose....and problems with the ground wire, etc.
A fuel pressure test will tell the tale.
Given that the o2s stopped going to 000 at idle with an increase in pressure, I am guessing that was the gauge and the o2 sensor is working properly. Given that they fall to 000 when driving and the car sputters, it seems to me that you have a fuel delivery problem. I would guess a pump problem but it could be electrical, or the pump hose, etc.
I am like Ronald Reagan, I only trust when I can verify