Do these work for the Phantom 3 pro? Also, when do I actually switch from let's say 4 to 16? How do I know that I need to switch?
I think that the threads are just slightly different between the cameras of the P3 and P4 unfortunately =/.
The point of ND is to achieve a proper exposure without having to adjust shutter speed. The general rule of thumb for shutter speed is to double your framerate (if you're shooting 24fps, leave your shutter at 1/50). This is the equivalent of having a 180* shutter angle on a film camera. Any narrower of an angle (faster shutter speed) and your footage will begin to look jittery (think Normandy beach scene from Saving Private Ryan). For aerials the effect will be more subtle, like weird stutters in the ripples of a lake if you're flying over water.
Normally, if you're shooting outside with your P3 pro, you would be forced to expose with your shutter speed: The lens' aperture is at a fixed f2.8, and you can't go any lower than ISO100, so you have to jack up the shutter speed and deal with stuttery footage. But with Neutral Density, we've just given ourselves another tool to expose properly.
To specifically answer your question, you'll want to choose the strength of ND filter based on what will properly expose your shot when you keep your ISO at 100 and your shutter speed at 1/50 (or 1/60 if shooting 30fps, 1/120 if shooting 60fps, etc.).
I find that ND16 (4 stops of light reduction) is perfect for clear sunny days. Sometimes I wish I had a ND32 (5 stops) when it's been really bright. ND8 and ND4 I will need if I'm shooting in heavy overcast or close to a sunrise/sunset.
A trick I use to pick the right ND filter is to fire up the drone with no filter on, find proper exposure with the shutter speed, and then figure out how many stops over I am. Example: My shot is perfectly exposed at ISO100 and 1/400 shutter speed. 1/400 is three stops of light over where I want to be (1/50->1/100 = 1 stop, 1/100->1/200 = 1 stop, 1/200->1/400 = 1 stop). Therefore, the ND8 filter is perfect! I throw that filter on, put my shutter speed back to 1/50, and I'm good to go.
Sorry if I'm more confusing than anything else, hope that helps =)