Car stumbles in reverse and jerky when accelerating from a stop

Hello, have you checked the EGR valve for proper operation? The EGR is not used at idle only higher rpm's, make sure it's closing all the way and not hanging open at lower rpm's. Also what are the fuel trim numbers at idle and 2,500 rpm? There's not much data to go by here, just what you're telling us. Those 02's look active, but there is that lean drop out there (lower voltage reading). So fuel trim numbers and 02 readings at idle and 2,500 rpm's to start with. A video of the live data would help much.

Okay, so I've watched the videos a couple of times and it's very hard to see the screen, but I see a couple of things right away. That fuel trim at idle, long term trim was at -12.5%. This means the ECM is taking away 12.5% of fuel at idle, that's too much. And the short term fuel trim of 99.2% is off as well. First thing I would try is cleaning the mass air flow sensor. But be very careful with it, they're fragile. Buy some mass air flow cleaner and a little brush. Make sure there's no carbon build up on the resistors. Another thing I see is that bank 1 sensor 2 02 sensor, it's pegged out full rich at 0.7 volts. This is the 02 sensor after the catalytic converter, it shouldn't be that rich. A back pressure test at the front 02 sensor (removed) should be 0-2psi at idle, any more than that and the catalytic converter is no good. But just remember I'm only going by what data I can see. But start with cleaning the mass air flow, give it a good look. The carbon build up is kind of hard to see.

One other thing, is I see that codes were erased 400 miles ago? Do you know what they were? If you do end up replacing the 02 sensors, make sure you get them from the dealership, aftermarket 02'sensors are junk and usually cause more problems than they solve.

Okay, I would have a good look at that intake air tube, Make sure there is no cracks or holes in it. That down stream 02 should be steady 0.5 volts or less, it's reading rich which might explain the negative fuel trim numbers. As for the mass air flow, it looks correct according to volumetric efficiency Chart but could still be an issue, I think you can unplug it and the car should run on a default strategy and see if that rear 02 comes down. Also make sure fuel pressure is 55-60 psi at idle and of course check for vacuum leaks (smoke test the intake if necessary). One last thing is how do the spark plugs look? If it's running rich they will have black carbon build up. I am concerned about the catalytic converter also, a back pressure test at idle should be no more than 0-1.5 psi. That rich reading post catalytic converter is a worry but cats are expensive so back pressure test first.

It's tough when there's no codes to go by, did you end up replacing the coolant sensor? It's best to get sensors from a dealership (OE).

I appreciate it but you don't have to send anything. The fuel pressure spec for this car is 53-60 psi. Since you have already replaced the pump, I would check to make sure it's getting battery voltage and has a good ground. And it maybe just a weak pump, but ACdelco is a decent brand. And watch what fuel pressure does when the car is stumbling. It may be dropping off. But that 45psi is low.

Okay, let us know what you find.