Your signature doesn't mention what year or engine on your E53. You have a diesel (so do I). When you start the car, do you first wait until the DDE (yellow) light goes out before engaging the starter motor? Does outside ambient temperature make a difference in the amount of smoke you see? Do you have this when you restart the car when the engine is warm?

If you replaced the "loo roll" breather with the vortex, that's a good long time upgrade (I've done the same). How clean is your air filter? What specific error codes do you know have when you read codes?

Oil, Castrol brand and weight isn't enough to be sure the mechanic put the correct oil in your car. It MUST be type that is BMW LL04 specification approved. Only a specific number of Castrol products meet this.

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2002 Euro X5 (E53) 3.0 diesel (M57)
5 speed manual with UUC short shifter.
Pre-xDrive NV125 transfer case (chain & gears).
Factory Xenon headlights, Spyder LED tail lights
Updated vortex crankcase breather.
Motorsport dead pedal, factory fire extinguisher, factory first aid kit, factory F&R mud flaps, factory PDC

Bilstein B6 shocks F&R
Redline oil has replaced "lifetime" fluids (F&R diff, manual transmission, transfer case and P/S).
Dimple magnetic drain plugs in all compartments.