Definitely replace the alt. as mentioned above. I bought on on eBay for about $200 or less. Its pretty easy to swap too. I think it took me an hour.
BMWs are finicky about power so don't put it off. In fact with the spikes you are seeing Id park it until you swap it. It's just one of those things thats best not to gamble with.

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740iLDUKE
01' DINAN 7 S62 Swap - Stratus Grau
(1587 produced in SG 440)
02' 4.6is DINAN X5 S2 Supercharged
833/3258 produced | 1/27 Dinan X5's