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First tip, make sure you have the correct gearbox fluid and diff oil. Second tip make sure you can undo the filler plugs before draining the gearbox or diff. I do know of someone who drained the box then discovered the fill plug was damaged and couldn't be removed without taking the box out of the car
The job is much easier with plenty of room under the car so if you can borrow or hire the use of a lift brilliant.
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Remember that General codes 30ff and PO112 are often symptoms not necessarily the cause
You refer to BOV ? do you have an aftermarket Blow Off Valve? the standard turbo actuators operate at 9 psi yet you refer to 19 psi. The higher the boost the hotter the intake air temp is which may well put it outside normal operating parameters and throw the code.
I would go very carefully back over the work done and check everything, vacuum line routing, make sure none are kinked absolutely no leaks.
I would also invest in a BMW capable diagnostic scanner it will give far more accurate information
Good luck sorting it