Yeah, I've seen also quite a few false alarm messages, some even funny like the one for Tele-Aid which I never had enabled, and countless front signal bulbs failures (bulbs always OK). I got used to the "moodyness of my car" , but this electrical issue scares me, cause once I got stranded (it was not MB) as I ignored warnings re. alternator issue.
I will check the auxiliary water pump, the noise is very rare and short -lasting when first started in the morning. The belt is fine and properly tensioned, I examined it the other day because I have a new replacement belt (the car has 80k).