Michel, welcome!

Upon re-reading your post it seems like a wiring break. Since you only get this problem in motion. This will be tough to find but some scouting might show where work has been done on the loom or maybe from installation of aftermarket electronics.

The other things that come to mind, make sure your ground connections are tight. Some of the items you mention are governed by the GM module, windows, wipers. GM modules are cheap and could be worth trying a swap.

As to help, the only good BMW indy I know about is in the north, Autohuis Buursema in Leek. If you are near there, you might try them, they seem capable.

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2003 4.4i black ext./black int./black headliner (kid's runabout)
2014 535d X-drive, M package, silver/black interior

Sold but not forgotten:
2009 E70 35d, black ext./black int./black headliner (sold 2021)
2006 4.8iS Le Mans blue/cream int./black headliner, SOLD in 2012 sadly...

Other hardware:
2015 Cayenne S (wife's new DD and definitely wroooommmmm)
2016 Tundra 1794 edition crew cab, luxo hauler
2005 Tundra crew cab, weekend hauler. Sold after 150k very happy miles.