DPFE is a common sensor to go bad on Fords, since exhaust heat gets to the sensor. Ford tells me they replace them all the time. The DPFE basically tells the PCM how much EGR is flowing, and the PCM adjusts EGR flow (via pulsewidth to the EGR vacuum regulator) to achieve the desired EGR flow based on that sensor.
EGR basically makes a motor run rough, which is why they don't engage the EGR valve at idle or at WOT, only at cruise speeds. An incorrect amount of EGR flow stemming from a bad DPFE could have the effect of making the engine run rough, most likely at cruise speeds. It could also cause improper spark advance, leading to pinging or possibly low power. I never thought about the DPFE causing a rough running condition, but it could I suppose. But Im not as sure that it could at idle.
If the DPFE code comes on because the DPFE correctly detects EGR flow at idle, thats a different story! EGR valves should never be engaged at idle, so any EGR flow whatsoever at idle will cause stumbling. A simple check here would be to unplug the EGR valve and cap off the vacuum line at idle, and see if the misfire immediately goes away. You could also monitor DPFE voltage and see if you're getting any flow at idle (if the sensor is good). Mine is normally around 1v at idle, which is zero EGR flow, so that's not my issue.
For plugs and wires, PLEASE stick with motorcraft wires, and either motorcraft or NGK or some other quality plug. No Bosch, no champion, etc. Any ignition misfire, whether due to plugs, wires, coil or whatever, will cause the engine to run bad in two ways. First, it's a misfire, that's obvious. Second, a misfire sends unburnt Oxygen right out the tail pipe, where the O2 sensor detects this unburned Oxygen, and assumes it's because the engine isn't rich enough, so it will increase the short term fuel trims to richen the motor up on that bank.
If the motor gets too rich, it will fuel fowl the spark plug, making the engine miss even more. The O2 sensor will see even more oxygen, and throw even more fuel at the engine, and this cycle repeats itself over and over. At some point, it's possible the O2 sensor throws a code, and once it does that, the computer will ignore that sensor and run on the base tune, which will return the truck to smooth operation. After restarting the truck, the computer tries to use the sensor again, and the whole thing repeats.
Idle surge can be caused by 3 different things: An increase or decrease in air, fuel, or spark advance. Since fuel is calculated based on airflow, the MAF sensor or vacuum leaks are the culprit here. Spark advance is based on load, which is determined largely by the MAF sensor as well. The computer will also use spark advance to raise the RPMs to compensate for a sudden drop in RPMs from some other problem. This sudden increase in spark can cause a rapid increase in engine RPM by a couple hundred. The PCM sees this overspeed condition, and pulls timing to fix it. Then, the RPM drops and the situation repeats itself. The idle speed basically "hunts" for a correct RPM.
Usually fixing the underlying problem fixes this condition. Typically, a misfire elsewhere.
As always, a good place to start looking for idle issues is to clean the MAF sensor, Idle Air Control motor, and put in new motorcraft plugs and wires if they're suspect. If you have a scan tool, pull codes and also look at the live data.