Right now, as I understand it, you can tap an object to set as the “far” point of the heightmap. Being able to set both the nearest point and the furthest would be really useful.
Honestly, Heightmap could be great as a postprocessing filter, with settings for “white distance”, “black distance”, and maybe even a curve for the black/white gradient (though I’m only mentioning that because the UI element already exists. Not sure how useful it would be).
Yep, this would be very usefull for adding atmosphere/depth/scale to a scene.
Yeah! Being able to set a gradient for it would be amazing (especially if you could set the alpha on gradient stops), but I don’t think there’s a gradient UI element, and I know UI elements existing already is a big benefit for getting features added. 
There is the same UI element for far / near blur amounts in depth of field post process - that could be used for white depth / black depth. A similar thing is used in other software for fog depth, giving a near to far effect on environmental fog 