Ive searched the forums and I end up at different parts of the engine with all the reading.

This is a 2011 N18 Cooper S, Typically makes this noise at cold idle. As soon as I give it a little throttle, just a tiny touch it goes away.

My brother mentioned air injection pump. Where not 100% sure if the Mini has one.

 

In my experience, whistling noises that go away with applications of the throttle or brake (when the car is sitting still) are likely to be vacuum leaks. Or other weirdness with air flowing through the intake and vacuum system.

The HPFP (the injection pump) that your MINI S has is very unlikely to make that kind of noise. From my reading here, it doesn't usually make noise when it fails, and that doesn't sound like the kind of noise it might make.

Open the bonnet and try to locate the sound. Use a piece of hose (or a "mechanic's stethoscope", which is almost the same thing!) held up to your ear and move the other end of the hose around, listening for the noise getting louder or quieter.

 

Im going to check in the AM. But I wont be needing a hose, its a loud whistle. I think the dealer said mine was replaced. Was there a recall on the HPFP?

Air injection pump used to heat the catalytic converter during cold start up. Not HPFP

 

Ok, so I made into my dealer today. Had a video of the whistle noise and my complaint of blue smoke after idling. The came back at me with a bad valve cover for both. Warranty wouldn't cover the cover, but my dealer did the right thing and covered it. Im so grateful.

 

Glad that your dealer good willed the repair and fixed it at no cost for you.