--Negative, that info is backwards. The wax pellet in the Fast Idle valve (if adjusted correctly to factory specs) should allow air to by pass the Idle Control Valve only when cold, before the engine is warmed up. Once the coolant get hot enough, it melts the wax and the valve closes, much like the operation of a thermostat.
I would put my money on a failing Idle Control Valve---Using a factory scan tool, I have noticed that while cruising at speeds, the IAC closes it self- If the IAC is 'sticky', the valve tends to stick closed even though it is being commanded open by the ECU during gear change or what not. This is more than likely the reason why it dies if you engage the clutch while driving. ---Try this, once your car gets up to operating temp, put it in neutral, or park and raise the RPM's to 2,500 for 20 -30 seconds. Quickly release the gas pedal and see if the IAC can open fast enough to catch the idle in time before it dies. You can do this test at a stand still.
Pulling the FPR vacuum hose off allows for extra air to enter the manifold, thus increasing your RPM's and smoothing out your idle.
As far as the slight misfire when all this is going on, I would look into your ignition tune, perhaps there are several areas that are effecting your drivability.
No codes stored yet?