When I have had computers freezing, the most likely culprit is usually the power supply. I know the one you have a good quality and powerful one, but it is the first thing I would try and swap out. In one case, I had 8 PCs I was building with a reasonable quality ($100) 600W PSU. These only had a mid-range graphics card and no overclocking. Every PC was freezing randomly. I was able to swap the PSUs for a different 550W model from the same manufacturer and the freezes were gone. Sometimes for some unknown reason, a certain model power supply doesn't work well with a certain model motherboard. There will always be a technical reason, but I have never taken the time to debug it.
If you can get your hands on a 600W or higher PSU, even if it is a much lower quality one then the current PSU, try it. With power supplies, if it is a good brand name, then you can expect it will supply the rated power. Without looking up the specs, I would expect your system is still under 600W. This is not necessarily a permanent fix - this is to see if your PSU is the problem.
A second common problem is the RAM. Some motherboards just do not handle a full complement of large RAM well. I have two identical motherboards here at home - one can handle four slots easily, and the other can only handle two slots of large RAM reliably - freezes with all 4 slots loaded. That is an easy one to test - just reduce ram to 16G. If it still freezes, take out the 16G and put the other 16G in.
If the CPU has not had the thermal compound applied well, it can be worth removing the heatsink, cleaning the old compound off, adding a small amount of new compound. I have come across PCs that were assembled without any thermal compound, but if the temperatures are OK, this is not my first guess.
It can always be the graphics card, and the only thing you can do there is to plug in another card (even if it is a cheap $30 one) and see if the freezing stops. It is not a very conclusive test, but if the freezing still happens with a low powered GPU, then at least you know the problem is not the GPU and is not a power supply high load problem.
The noise is rectified mains noise getting though to the motherboard. It is the sound of 100/120Hz plus lots of harmonics. It can be an earthing problem as suggested, or a fault in the PSU.
Disconnect any external USB devices, such as printers, that have their own power supply. Powered speakers. Ethernet connections wouldn't be the problem. The monitor could be - try replacing it temporarily.