P0215 is a code for the LP circuit. The ECU is seeing an out of range condition on either resistance or amperage draw likely resulting in reduced or no operation. Could also be cause by wiring failure, connector failure, bad gorunds, or bad battery connections.
I miss typed that one, it was actually the P251
You cannot tell if the LP is operating correctly by looking at the filter. The CP-3 will attempt to draw fuel and as long as the LP is stopped in an open position it will. If the LP stalls\stops closing off the intake port the truck will not start as it cannot draw fuel. To vlaidate LP operation requires a gauge on the CP-3 inlet to verify there is positive pressure all the time, at a minimum 3 psi and better 5-8 psi all the time.
Good to know, I would like to install the test T and quick connect to test the LP pressure.
FCM is an acronym for Front Control Module, basically has nothing to do with the CP-3 or fuel system. What you are trying to describe is the FCA, Fuel Control Actuator. Urban legend that shaking it will tell if it is good or bad. They can be good\bad if it rattles\doesn't rattle. The typical problem with the FCA will show as inability to maintain high rpms or dying at an idle and\or loping.

Again another miss type, but your assumption was correct.
No start conditions have some definite starting points. You have to verify you have constant fuel pressure to the CP-3, gauge in the fuel inlet. Next step is to verify you are getting adequate rail pressure on cranking, the ECU will not even fire the injectors until it sees somewhere around 3000 psi.
Lack of rail pressure can be a lot of things, you have to go thru the steps to find the issue or it will resurface, only a matter of time. The rail PRV is a good candidate for low rail pressures, as is low batteries, bad battery conenctions, bad power signal to the ECU, bad chassis grounds, failing rail pressure sensor, bad harness, bad FCA, bad COV, bad CP-3, and ECU failing.
Certain trucks have an issue with the AC compressor activation wire in as much as it will rub on the chassis and partially short throwing all manner of garbage into the electrical system causing hard\no starts, bad idle, APPS codes, etc. Bad connections on the battery or a failing battery will cause the exact same symptoms and there is no good way to tell them apart.
A shorted fan will shut the truck completely down, as will a loose or shorted wire on the OBD port. If you are not getting a CEL and bad driving manners from the APPS codes I would start with check harness and battery and ground and power connections and having the batteries load tested.