Your questions depend on a lot of factors. Modern lidar systems usually work with a “return” system (no official name). Imagine you shoot with two lasers at the wall in front of you. One laser travels to the wall and back to you. Another laser has to pass a membrane (or a piece of paper - or leaves of a tree!) so you get two signals back: one deflected by the wall right behind the membrane and one of the membrane itself. Creating the difference you get an overview of what the treetops look like as well as what the ground underneath looks like. You can have an arbitrary amount of return values, more make things more complicated though.

The range depends on wavelength and wattage. In theory you can go up to a few thousand metres, usually you work around 200-1000 m when going airborne. Terrestrial you usually go for less than a hundred meters to have a high point density as well. This also kind of answers the last question: if you go higher, your point density will be lower. In some cases it might make sense, especially if you’re looking at mainly flat surfaces (still, depends on the use case) but in rough terrain you want to digitise you might want to chose a higher point density to replicate real world features more precisely.