Generally, you would only hear the coil whine under load, and usually at very high FPS such as loading screens, ect. It was just a thought, and the fan speed you mention makes it sound like its not the coils. I wonder if it's a defective fan/bearing.
You should be able to leave the pads on, they mostly stayed on the HSF assembly when I removed mine. If you replace, you would need to know the thickness of each pad area, as they come in different sizes, such as .5, 1.0, and 1.5 mm. You should be fine whichever way you place the compound, unless you put a ton on or a tiny amount, you'll be fine. If you have enough compound, you could always place some down, install heatsink, and remove to see how it spread out. Then clean and apply again.