1995 E420 Low "Fast-Idle" and hard start

[Holson Adi]

It's a 1995 E420 with 92,000 mi. on it

The car is going to the dealer next week for a check on this problem but while I wait, I'd like to do things myself as much as I could.

Symptoms:

on cold mornings and cold starts, the fast idle speed seems to be 100-200rpm lower than it used to be (it's now at about 900rpm instead of 1000-1100 rpm like it used to be)
it does however start fine.

on non-cold-starts (warm/hot), very often, it would just keep cranking and not fire up until I give it some throttle then it fires up and chuckles (too much fuel I guess).

If I press the accelerator pedal slightly before and as I start the car it cranks and fires up nicely all the time (makes nicer sound too )

doesn't stall at all even with AC on and at high temperatures, no unusual idle problem, no problems with power or mileage.

Things that have been done to it that might be related:

New starter motor (could the dealer that put it in have fiddled with something?)

I took the LH module out and put it back in
New rotors,caps and plugs and air filter at 87k mi.

=========
Any ideas?

I will change out all Four 10A fuses in the module box and check the air filters

the car does not have an OVP or Fuel Pump Relay, right?

oh one more thing,
Is the engine computer supposed to blip the throttle slightly as I crank it when hot? because it seems to only do that when cold...