I would not switch to a three pin fan on the cpu heatsink , the four pin header for the cpu fan is there for a reason.
By getting a new fan the noise will also go away.
I don't think it will. It has to do with the PWM function and how it slows the fans down. Running at full speed you don't hear the sound because of the function not being needed.
You can run a 3 pin fan there perfectly fine, I have 5 computers in my house running on 3 pin fans for the CPU just fine. The motherboard is actually designed to work with them as well as 4 pin fans.