Not many here have too much experience with E53 Diesels because most of us are State side. I am assuming you are in the UK. So with that said, just have to go off of regular stuff. Black smoke from a diesel turbo usually means your turbo is cooked. Oil is leaking and is being shot out the back. but again, it could be other things as well, but with that many miles, normally is when a turbo will begin to fail Depending on how hard it was driven in the past, if the last owner did hard pulls with it and then shut it off immediately, oil that sits in the turbo begins to burn.

As for the door, not working, sounds like a door handle carrier is broken. Hopefully other UK'ers will chime in to help you out.

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2011 E70 50i M Sport