Please help me understand rendertextures as terrain heightmap

I am currently using SetHeights() to to apply heights to a terrain.
It works, but its a little slow. I have read on several occasions that it would be faster to use CopyActiveRenderTextureToHeightmap(). But I cant really find much documentation on how exactly to do that and what exactly it does.

1. how must the rendertexture look like to be used as heightmap? I guess width and height is just the terrain resolution, what about depth and format?
2. I never used rendertextures before, so how do I actually get the data into the rendertexture? I just have them in an array suitable for SetHeights(). I calculate the heights in a shader, so if I could avoid a readback to the CPU that would be great.
3. Why is this method faster, what is the difference?
4. Could I do something similar with Alphamaps? How would that look like?