Very high idle at start, slowly idles down after hot. Replaced ICV, sometimes lopes, can shut down, restart, idles right.

Always worth rechecking timing but I am guessing you have another problem though I can't imagine what it might be. The surging you describe was a problem with mechanical constant injection systems of 10 - 20 years earlier than your car; maybe air leak, dirt in the injectors, poor spray patterns, low fuel pressure...

Remove the gas cap,and then remove the return fuel line off the back of the throttle body.Now take a air hose and blow in the line you removed to make sure it is not clogged up,you should be able to blow back threw the tank easy with compressed air.If you are able to,then replace the fuel pressure regulator on top of the throttle body.

On some engines the icv is inside the intake manifold and is suppose to move open and closed to vent in extra air for idle. Sometimes they get carbon in the port and the valve sticks. WD40 will dissolve the carbon.

The Code can also mean the coil inside the icv is fried. A simple power off ohmmeter test can test the icv. Check for you tube repair videos

It will deffinitely have a form of idle control, sometimes it is part of the throttle body but there will be one... 100% certain.

Rough idle as in lumpy will not be an ICV related fault, as with ICV it will either have solid high revs or none at all.

It will either be an inlet vacuum issue - split hose, gasket, MAFS etc or an irratic voltage caused by things like a Lambda or worn throttle potentiometre

Describe the rough idle in more detail if you can, also are you UK or USA etc.

Do you know what cc and engine code your car is?

most common problem is an IAC (idle air control) motor and computer reprogramming

could be the coil pack playing up ,or the computer not working properly ,very difficult to diagnose without the right software so i would suggest taking it to a dealer and see what they say

If the car is having trouble maintaining idle (the tach dips and car dies) the common causes are the idle control valve and camshaft position sensors. The cam sensors failing will be indicated by a check engine light.

The ICV can removed and cleaned with good results (I think there is a write up on bimmerfest) or purchased new for about $100.

While you are in there check the intake boot that is Y shaped for cracks, it's prone to fail and will mess up your idle too.

read up on the major forums and you'll get more info

fuel regulator?

have u checked for upper intake leaks? use a can of carb spray and spray around base of upper intake, u will know if u have a leak righ away.

Here is the most common cause of surges and stalls, it is the idle speed control air-bypass valve and throttle valve, they get full of gunk over the miles and cause idle issues (stalls) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.