Help With List Of Issues On Focus 1.8 Tdci Sport

Hi all

Owned the car for about 2 years now and its been a love hate relationship, there is somthing not quite right but no garage as of yet has managed to sort it. Which is a shame as when its behaving its a great car and its only done 50k miles :(

The car has been checked loads of times but never shows any errors, even had an update from ford which has seemingly made no difference at all.

Its recently had a full service with plugs, fluids, filters including fuel filter.

In no particular order:

1. The car has a problem with cutting out, usually when you 1st start it, will run for maybe 15 - 20 seconds then the accellerator becomes unresponsive and the car just slows down and cuts out. Once restarted its then fine for the rest of the journey.
   
2. Fuel consumption seems to be rather low considering the car, on a decent motorway run sat at a constant 70mph it struggles to make even 45 mpg, now im not expecting massive MPG but compared to older less efficient TDI cars I have owned this is low.
   
3. Battery seems to discharge rather quickly, its now on its 3rd brand new battery and 3 months ago had a new alternator due to the previous one burning out. If you leave the car for a week then it struggles to start. I noticed when locking the car that the green display on the dash remains on constantly, is this normal?
   
4. The car has been parked up in our garage for 2 weeks while we were on holiday aside from the problems mentioned above it was running fine, engine pulled hard no issues. Upon jump starting the car (due to a flat battery) straight away the turbo now makes a loud high pitched whine and slight lack of performance.
   

Car was in the garage yesterday to be diagnosed and came back with a report of no split hoses or boost leaks and suspected turbo failure.

Now I have had turbo cars in the past both petrol performance ones and TDi ones and have had turbos fail, but never after being parked up and not driven for 2 weeks. Just seems rather strange to me?? Yes its been very cold, but surely that cant be a problem??

Any help and suggestions would be great, dont want to have to sell the car but this is starting to get rather soul destroying :(