Is this an automatic or manual transmission?
A normal 3.0 manual transmission truck will prop the idle up at 1500 rpm as long as the truck is still rolling. The idle will drop to about 7-800 once you pass through about 5 mph toward dead stopped. This is "normal" PCM Programming to aid in shifting, Ford's better idea.
Many have played around with different size holes in the IAC gasket to get rid of that "feature". Another cheat is to put a switch in the VSS signal wire to the PCM. Flip the switch open, the idle drops. Pointless, but doable if you like to use old-school engine braking.
What you describe sounds like you may have a vacuum leak. Pay attention to your HVAC Controls AFTER you shut off the truck. You should be able to hear the different actuators move when you select vent/floor/defrost for a minute or so after you shut off the engine. If that doesn't happen, you may have a bad checkvalve or broken tube to the vacuum reservoir (sphere under the airbox). Sometimes the tube gets a pinhole from wearing against some metal. That's usually a pretty small vacuum leak, really too small to affect idle.
The very common vacuum leak on 3.0 is at the back of the driver side (?) rocker arm cover. Look for a rubber 90 degree elbow to the PCV Piping. Those are well-known to deteriorate and cause idle issues due to vacuum leaking. It's been a while since I looked in there but I recall there is a replacement elbow in the HELP section rack at many auto parts stores.
Another easy check is the air intake tube from the MAF/Air Filter box to the throttle body. Look for holes in that tube, loose clamps, etc. The PVC connection there can leak as well.
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