It looks like your initial diagnosis was pretty accurate actually. He clearly stated that he replaced the BPA (brake pedal assembly) after which the car developed the problem. There was no doubt about your recommendation concerning lubrication and the actuator rod mechanism to the brake booster: that was exactly where the car's problem was. When the BPA was replaced, the retaining and actuator mechanism as well as the BPA as a whole had to be assembled correctly and lubrication done in specific places. BPA can get stressed (or warped) by bolting forces and can easily create "grabby" braking effects which results in vibration noise that is exaggerated through hollow steering column and other metal parts and the bracket itself to the firewall (very thin metal component part of BPA). Colder and humid conditions could result in similar vibrations within external braking parts (rotors, caliper pistons, pins and pads) especially when the car isn't being driven (again "grabby" effects result in vibrations that are echoed through metal parts and through hollow tubes right into the driver's hearing). As far as the loose braking (he puts it differently: "sunk pedal" would be a different issue namely brake fluid dynamics as well as wheel brake parts and not BPA- actuator rod-booster issue. Lastly, he mentions new struts and shocks: again a different issue: incorrect struts installation (which are bolted to the knuckles which hold the braking parts) would also result in different symptoms such as misalignment and other noises. This was a great question because it spoke of a very unique type of noise that may or may not resolve on its own.
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Friday, June 4th, 2021 AT 8:44 AM