I'll do the best I can:
Just as the clutch is starting to contact the flywheel, or before?
As it's starting to contact
Just as the trans starts to turn and the car is starting to move?
Yes
Does it do it when cold with the clutch already pressed while you start it?
I don't hear it when starting the engine and clutch engaged.
Does it do when when cold and you start it in gear with the clutch in?
I have not tried this
How about right after you start it, then shut it off and restart does it do it again?
Have not tried this.
Sorry I could not answer a few. This just popped up and I found this thread in a search.
