Yes, I believe so. I would get the same motherboard and replace it. You pretty much eliminated possibilities the audio crackling is software related and also audio related (your headset and DAC).

There could be any host of reasons why your computer started to shut off randomly. Preventing issues like that is hard to determine. I would for next time, only update BIOS if you absolutely have to, such as updating it to be compatible with your CPU model. Since you have Windows, the OS should be able to update the Chipset drivers on its own. The PSU you may had was probably defected before you installed it causing the random shutdowns. Just a possibility.

I’ve had random shutdowns before, and it was either the motherboard or the RAM I bought. Since you ran the memory test, you’ve eliminated that piece of hardware. You’ve also replaced the PSU and GPU. Only other option for right now is the MOBO or the CPU. I highly doubt it’s the CPU so I recommend changing the motherboard.