Have you considered taking the car back to the dealer you bought it from? You also say the turbo is running, this isn't possible when the engine is off and it is the cooling fan or turbo water pump which can be heard for some time after the engine has stopped. Has the car had the recall for the turbo water pump?
With regard to the poor running and starting, this could be excessive coke build up meaning the engine won't function properly in terms of the way it takes in air and fuel and emits gas. How many miles has the car done? You could try using a fuel additive product called BG44k, some super unleaded and, if you can get the car running, a good blast with some revs. In my opinion, these engines need to be used and don't appreciate light use. I hope you are able to sort these issues but be prepared if the car is not under warranty as it could be costly.
Many thanks for your reply. The car was purchased just under 48,000 miles. The car was taken back to the dealership Masterdriver Ltd in Buckinghamshire (Not BMW Mini Dealership but apparently a Mini Specialist Centre) on two occasions because of several issues and or faults which I addressed to the finance brokers because my Husband and I werent happy and in some ways still arent.
There is a note on the paperwork to say about a pump replacement and when the car was purchased, due to my concern about reading about and of 'the mini death rattle' the dealership put on a modification part.
The car's paperwork looks in order in regard of it being serviced by the last owner (at BMW Mini - Scotland). The car was purchased by Masterdriver Ltd and advertised and I purchased it at the end of July. Out of the issues and faults, I also mentioned this juddering when taking the car back to Masterdriver Ltd which the car experienced after filling up but started.
One of the dealers that run Masterdriver Ltd told me that the car needed to be run at least every third fill up on super unleaded and they had had several other purchasers come back with the same problem. My Husband and I continued to fill up with super unleaded from then (and not do a super unleaded fill up every third fill).
The car also had (amongst the issues and faults that we addressed Masterdriver Ltd) a crankshaft oil leak and rocker cover gasket seal needing replacing. On collecting the car, we took it to a garage we use for any repair and or servicing and found that things were not done hence addressing the finance broker and finance company.
I recently found an oil leak on the drive and a smell of 'burning rubber' omitting from the front driver outside area of the car. I took the car to the garage who suspect two further seals in the engine and who topped up the oil and with me are monitoring any further oil loss.
This week, the car began to judder and conk out (stall) and despite getting started by revving the engine, some black smoke coming out of the exhaust, the car started and the black smoke stopped. This happened on return (and short local journeys).
This morning, my Husband started the car and found the car juddering even worse and not starting at all. Black smoke still omitting from the exhaust. For the first time a light has come up on the dash saying 'service.'
Despite the fact I live in South Wales, the car was originally purchased, owned and taken to a BMW Scotland Dealership in regard of its servicing and or parts and I will contact them today to check on what the car has had and or has done.
If I manage to get the car started to get it to the garage, I just want to feel some assurance that I'm not causing any issue/damage to the car or is it best to get the car towed (which I will have to if it doesnt start in any case).