Congratulations on the SDL purchase, these are GREAT cars.
Some Black smoke under full throttle is normal and you can expect some grey smoke when first starting from cold at idle. Any excessive smoke at other times may indicate that oil is getting past rings, valve guides or turbo seals. Your Turbo is running all the time but really adds boost at 2000rpm+.
The Auxilliary cooling fan in front of the Rad. should only kick in if the temperature is getting to the 90deg+ range, it certainly shouldn't be on all the time. There is a sensor that switches it in at high temp. This may be faulty.
If the A/C Compressor is not engaging then first check Fuse #5. If this is blown there could be a couple of reasons. Shorted A/C Compressor clutch, or seized Auxilliary Water Pump. Unfortunately one can cause problems with the other (this happened on my SDL) as they are both on the same circuit along with the Automatic Climate Control (ACC). Check out both items in turn to see if one has a problem. The Aux Water Pump is a common problem and a pain to fix due to its cost and location buried between the two engine bulkheads. Disconnecting it is the best temporary fix.
If your performance is reduced when the car is warm, there could be many reasons but I doubt that the injection timing is out as this would affect the engine hot or cold. Undo the oil cap when the engine is running and up to temperature to see if there is any pressure. this would indicate "blow-by" due to worn rings or valves guides. Your car may just need an "Italian Tune-up" (do a search on this) if the car has been driven sedately and coked up the head. A compression test (hot) will also indicate any excessive ring or valve guide wear.
Can't help you with the antenna question, but these units are prone to failure so you may want to see if it works at all before you wire up your sound system to it.
Use the Search function here for further info and good luck with the car.
