I am attaching 2 pictures.
I am trying to figure out the name of this part and exactly what it does. I know it has something to do with emissions. Coming out of the little canister is a rod that moves in and out and i believe it somewhat controls the idle speed.
It does also have a two prong electrical plug.
When starting my car cold the engine revs up for a few seconds and then down to nearly stalling. It does this for about 5-minutes and the goes to a very low rough idle.

That'* your boost control valve and solenoid assy.

I would start by checking hoses for vacuum leaks and if none found check TPS operation.

Thanks, I still have a small leak on egr tube. I have brazed a crack in it twice and apparently i have to braze it again. It is still leaking air.
Is the boost control valve for the supercharger?

Yes it works with the supercharger and vaccum system