There are several possibilities but we will start with the most common. The EGR valve can stick open on these causing this exact symptom. You can remove the egr valve without too much trouble to check it. The valve is mounted in the front of the intake manifold just behind the air inlet from the intercooler. Remove the two 8mm headed bolts and the connector from the valve. Now take a big screwdriver or prybar and rotate the base of the valve counter clockwise. You can pry the mounting tab away from the air inlet housing. Now you can pry up on the mounting tabs or under the lip of the valve being careful to remove it straight up. If the valve is stuck open with carbon, clean it out the best you can and make sure it shuts. If it is stuck open and there is nothing holding it open, you will have to replace the valve. Let me know what you find and I will help further.
There is only 1 pump, the one on the frame. The only true test of the fuel pump is a pressure test. If the upper housing is filling up, the pump is at least working. Most likely it is not the egr valve. The fuel pressure could be low and causing the injectors to fail, but the pump is not going to directly cause the miss.
It could be fuel, but not likely. More likely than fuel pressure would be faulty injectors or a faulty injector control module. We have been having some issues with the injector control modules also, the only way to diagnose this is with a good scan tool that reads live data from the computer. Sometimes the module will also set a code. If you had some really bad injectors it could also cause this, but this is not as likely.
It could also be a problem in the high pressure oil system. We would need a good scan tool to diagnose this also.