Part 3:
After several days with no issues, I assume (or at least hope) that the amplifier is fixed/cured.
Opened up the amplifier again and coated the pins on the HBCD412A circuits and the nearby area with silicone coating for electronics (422C from MG Chemicals) as well as applied new thermal paste on the HBCD412A and on one of the voltage controllers (indicated on the picture by red circles).
Awaiting the splash guard as well as a Pingi Moisture absorber that will be installed at arrival.
Some side notes:
1: Thermal paste: The expected lifetime of a high quality thermal paste is 2-5 years! Is the change of the thermal paste a part of the BMW service schedule?
2: The last incident with popping and crackling noise from the speaker system, was so loud that it hurts. Since at least one hand is required on the steering wheel, I was not able to protect my ears with my hands. The sound/noise was picked up by my Apple watch. Under a layer of a fleece jacket and a down jacket, it recorded ~105dB for ~4 minutes. I would claim that this is represent a traffic risk/hazard, especially since one are not able to shut off the amplifier. The only options is to stop the car and pull the fuse.
3: To me it seems like if one pull the amplifier fuse right after the first incidents of popping and crackling noise, one might be able to save the amplifier by opening it up, clean it, apply some coating and re-apply thermal paste (and install splash guard).
4: It might also be beneficial to install a moisture absorber, in order to suck the moisture out of the air, as well as absorb water entering the amplifier surrounding. Need to gather some experience ...