These strange happenings are sometimes the indication of the battery and/or voltage regulator/alternator nearing or at end of life. Low system voltage can cause premature FSU failure.
These cars, most BMW actually, will start and run OK with a failing electrical system, but other accessories will start showing issues. Have it checked before the GM, general module, decides it has played along long enough.

Initial problem does sound like a failing FSU, but it only influences the AC fan normally.

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