Sorry for your probs with your cars man! Not sounding good bro
It's hard to find out whats wrong when the cars not in front of ya, but I'll try and throw in some suggestions.
Similarly to Exilion, that sounds to me like the engine timing isnt right. Rough idle together with cut-outs and your spark plugs not burning all the fuel are all signs of this. If the idle revs settled when you had it running roughly, do you recall the speed of the idle, is it higher or lower than normal?
You may need to retime the engine. If you are not too good at mehanics I would suggest you take it into a garage for a diagnosis of the problem and maybe a quote (this will be higher than you want it to be).
(I don't know what quotes cost in the US but in the UK they are cheap and sometimes free. If they're cheap in the US too, get several quotes from different places [less chance of them faking what the fault/cost is]
Also, do you remember the engine ever overheating? A result of bad timing can cause an engine to overheat which in turn could have caused the head gasket to go aswell, causing the white smoke (like numark said).
As I said these are just suggestions that maybe you should check out so don't panic, I am by no means a pro but I've had my fair share of disasters, and I never like to part with my cash when I can fix it myself for 20x cheaper.
Yeah, and be careful checking those plugs, most spark plugs produce like 50,000 volts! (You need to remove the plug from the engine, connect it to the wire, then press the thread on the plug against a metal part of the engine block. obviously, keep your hands well away from anything metal on the plug or car).
Anyways I hope this helps and good luck, I wanna hear that the bimmer is back on the road where it belongs
Keep us updated.