You have secondary air pump error codes and are not eliminating the secondary air pump as the cause? Certainly there could be another cause but your symptoms are exactly as those caused by a failing-failed secondary air pump. You have symptoms and verifying codes.
BMW Secondary Air System Fault Code Diagnosing How To DIY OBD-II | Bavarian Autosport Blog
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 X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
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