Whirring Noise - Poor Idle - Bad Gas???

Last week my 99 MX5 one day started to stall when I came to a stop. Or as son as I touched the gas pedal again. It did re-start OK. I also noticed a (I hate describing sounds) whirring noise coming from the engine for 10 to 20 seconds at COLD start up. I had a ½ tank of regular gas the next day the wife drove it to the gas station and it stalled repeatedly she filled it up with premium and added a bottle of STP Gat Treatment after a mile or two the staling seems to have stopped but I still have the whirring noise at COLD start up. They came together but I guess that they may not be related? Any Ideas??

Vacuum leak would be my guess.

Did the car kick a check engine light?

I'm guessing the noise is unrelated. No more stalling since the STP Gat Treatment?

Correct it’s not 100% smooth but no staling, the noise almost sounds as though something were just touching a fan or belt (it defiantly is not) it decrees quite quick but it does have a slight ticking now though, maybe what I grew up in England being called tappets’ but here I think you call valves?

I couldn't find a Vacuum hose visibly damaged or broken and thought that was a good idea so i went right out and looked.
No check engine light and over the 3 days it staled at least 15 times. STP GaS Treatment and 1/2 tank good gas?

You might want to try a Sea Foam treatment....may be crud in the injectors and/or intake.