Problem has been solved by the same dealer a while after my previous post, it was the Brake Light Switch, on which many W210 users had complained in the past. Now the car runs as it should

~Nautilus

__________________
1990 260E Sportline (that's 300E 2.6 for our American friends) -> sold
2001 E320 4Matic Elegance -> my Dad's daily drive
2005 Seat Leon FR 1.8T