I got BMW E92 320i and have all the same symptoms:
engine warning light pops in, engine shake, lack of power in low revs
and the fuel consumption 28 mpg instead of 37 mpg + very bad oil lick.
The car was in BMW Berry in Cheaswick-London 2 times already and it's there now for the 3 time.
First time they keept the car for two days without knowing what happend and running 50 miles test during the night. They find out that I have faulty injector and the sensor. After they chang it under warrianty the car run ok for a week!
Then the shake came back straight on again. I went to check the car with them after about month and a half and they said the problem is oil lick from the gear box but is not big enough to do it under warrianty. When I did ask why the engine is shakeing they said nothing about last repair of the injectors and the sensor they just said that the oil licks on the electric cables and that couse the problem.. so they send me home with shaking car and oil lick
Now after another month is back again to the BMW garage in Berry Chiswick
and they running some tests for the second day without saing to me what is wrong.