The EGR valve is supposed to open only in the following conditions: engine warmed up, and rpm's above idle at part throttle, but never at full throttle. Basically, only when you're cruising. EGR puts burned exhaust gases back into the intake manifold, and this helps with mileage and emissions. EGR valves by nature get carboned up over time. If this carbon causes the EGR valve to stick open, it can result in a serious stumble at idle.
The EGR valve gets vacuum from the intake, with an EGR valve solenoid in line. This solenoid makes or breaks the vacuum connection to the motor, depending on what the PCM commands it to do. A simple way to check to see if the EGR valve is sticking is to apply vacuum directly to the EGR valve via a vacuum gun. If you don't have a gun, bypass the egr solenoid and that will hook vacuum up directly all the time. As soon as you apply vacuum to the EGR valve at idle, the engine will immediately run like crap. If it's already running like crap because of a stuck EGR, then I guess you won't see a difference.
You can remove the EGR valve and clean it with carb cleaner and a brush. That doesn't cost much, just a can of carb cleaner and a new EGR valve gasket. Sometimes you can ever reuse the gasket if you take it off carefully. Not a bad idea to do, but I doubt this is your problem. How hard is this to do? I am a novice of sorts (brakes, spark plugs, fuel filter today)?
What do you mean it says system management recharge?? Where my digital info is (mileage, mpg, trip etc) it says something "system recharge" or something like that (it flashes really quickly)I have never heard of that. What's saying it, and what exactly is it saying?
Both of your engine codes mean that both engine banks are lean. This generally means you should be looking at either vacuum leaks, bad intake gaskets, rips or tears or loose clamps in the air inlet tubing, etc. Any time air gets into the motor without having to go thru the MAF sensor, it's unmetered air, and that is a problem. The engine won't know that air is in there, so it won't add any fuel for it, and voila you have a lean condition.Is it possible that cleaning my MAF sensor didn't do anything because the MAF sensor is bad? How would I check this?
Another possibility is a lack of fuel pressure, a clogged fuel filter, a bad fuel pump, a bad fuel pressure regulator, etc. I think if it any of these I will have to have my mechanic look at it because i wouldn't know where to begin...
If you had the right tools, I would say do a fuel pressure test first, and a visual inspection of the air inlet tubing for holes or loose clamps... any leaks. If that isn't it, I would get a can of brakleen, and in the morning when the vehicle is cold, I would start it up and spray small amounts of brakleen onto the intake gaskets. Any rise in RPM indicates the motor sucked in the brakleen thru a vacuum leak, and shows your problem area. Intake gaskets are known to be an issue on 4.0 engines, especially when the motor is cold.
The TPS could be a problem, but I doubt it. Lets leave that test for later. A TPS problem will cause a rolling idle, but usually not a lean code. Think vacuum leaks. Check the PCV valve and grommet too. If you haven't already cleaned the IAC valve, you can try that as well. Not going to fix a lean condition, but could help idle stability.