We always check the radar on the taxiways before departure, especially in Sao Paulo and also to overcome the problem you wrote with the intensity knob.
For the advisory about cab press., I assume that's because in case of triple ADR fault, you lost CPC1+2, so you have to manually control the pressurisation, then it could a advisory about cab pressure rate because it's very difficult to adjust it when you decide to descent for example.
So for me there is no sign of rapid decompression.
In my last recurrent training, we had a double ADR fault and the flight instructor gave a third ADR fault just for fun, eventually we manage to land but it,s very tricky. The instructor told us after that we were in the group of survivors ( around 30 %), and we were not at FL350 and not in the middle of the ocean and CBs.
What i don't understand is why the PRIM1 and SEC1 disconnected, probably because of strong turbulence.