2) Is the Automatic Pressure Control Mode doing it's work correct when "Packs Off" tkof is used?
I am asking this because I noticed on our aircraft a very high v/s (-1000ft) of cabin rate after the first pack is switched on.
During the early climb the pressure controller is expected to limit the cabin
climb rate. If instead a cabin
descent is initiated I'd agree with you that there is something wrong. A fast cabin descent during a/c climb would only be necessary if you switch on the packs very late above lets say 10.000 ft.