Problem on every first start (idle and clutch) [Video]
 

Hi people, I've been experiencing this problem for more than a year now. Took the car to two licensed repair shops, they couldn't find the cause of the problem. So this is what happens:
Every day, when I start the car for the first time that day (cold or warm weather, doesn't make a difference), it starts up normally (without a stutter etc.), drives normally until I press the clutch or put it in idle, that's when the rpm just start to go up and down until it hits zero,and the car turns off (not totally but kinda like the start/stop system), then usually (not always) the Start/stop system icon appears on the screen, and i have to press the ignition button to start it (if i keep the clutch pressed, and don't push the gas pedal, sometimes it can't start, like in the video).
The car does show from time to time the yellow engine light, which at the repair shop they told me is because of a problem with the oxygen sensor. But I think it's unrelated?
It's not a big problem, because i realized that the solution is just to stop the car and turn it off completely, and then start again, and everything works fine. But it is pretty annoying. Hope I described it well, ask if it's a little confusing
Here is an example video i recorded for the mechanics that tried repairing it to see. drive.google.com/file/d/0BxdFHH8DMqC4YllwNVZmRGkzT1U/view?usp=sharing
If anyone knows what is the cause, or has a some advice, please help

Yep, there is definitely an issue going on after viewing your video. These licensed repair shops, were they MINI certified? If not, I highly recommend you take it to a MINI specific indy shop. Use this website to help you find one: Mini Cooper Repair Shops - Find a Mini Cooper Mechanic. If you're getting a CEL because of a bad O2 sensor, replace it and go from there.