BMWs are very sensitive to low or high voltage and cause error lights like you are experiencing when there is a charging or battery problem. I assume you replaced the battery with one that meets BMW spec as does the alternator.

I would monitor the alternator output using the OBC to see the charging range or if it is spiking. 13.9 is about the max your alternator should be putting out. Running down the highway it is usually in the 13.3 to 13.6.

Check the battery with X not running it should read around 12.6. with nothing on.

It sounds like the alternator is a bad one.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas