What is the recommended usage differences for ND4, ND8, ND16, & ND32?  Do they just darken bright light?

ND filters are not required on a Phantom camera for taking still photos, the automatics will take care of bright ambient light conditions just fine. They are advised for video work, in particular to get the shutter rate down to approximately twice the frame rate, so for example, if you are shooting at 30 fps, then ideally you want the shutter speed to be 1/60.

The reason for getting the shutter rate down to this vicinity is to try and reduce movement artifacts in the video by allowing a small amount of motion blurring in the video. The technique for selecting the right filter, is to fit what you think is the right filter, fly up and do a test and look at the shutter rate as displayed on the screen while the image is correctly exposed.

To correctly expose the image, I use the histogram display and adjust exposure using the exposure thumb wheel on the RC unit. If the shutter speed is above the 60 fps, as in the example, then you land and fit a darker ND filter and try again. If the shutter speed is under 1/60, then fit a lighter ND filter.

Yes, but as a result, they help you to remain the proper shutter speed (which should be a FPS number x2: 1/50 for 24FPS, 1/60 for 30FPS, 1/120 for 60FPS) with opened aperture.

Please refer the reply of 2#. And it depends on the weather and lighting condition. Different filters are required to adjust the light to get better performance.