First ever Mini and some advice required please?
 

Hi All
I've just bought my first ever Mini, an April 2007 Cooper, and drove it back from an indy dealer in Wales to Sussex.
Great drive on the motorway, but once you hit the lumps and bumps, you do feel it! and once I got to a full stop, when I got to junctions or Traffic lights, the car kept switching off; yes there is a start/stop button, but am I right in thinking this is for when you start/exit the car only, and doesn't affect the car during it's drive?
The next day I spoke to someone about it, and they said their BMW did this when it was warm, it's like a fail safe to keep the temp down, and as on the way home when I went round roundabouts the oil light came on, off on the straight though! as well as the dreaded yellow engine light; I topped up with oil, no red oil lights now, but the engine light is still there, but no longer switching off in heavy urban traffic situations, so far! (but could be not heated up enough)
So if anyone can confirm about the start/start and a way to get rid of the engine light, would be a great help!