1) If you own the professional edition, you can use the automatic LOD system for Terrains. And terrains are split into chunks, which in most cases allows to cull big parts of the terrain. Also one could theroretically render without indices as triangle strips, which is again a bit faster than the standard aproach with indices, although I think that hmps use indices...
So the one big advantage is that gamestudio is able to get rid of quite a few triangles, without any efforts from your side in comparison to models. The disadvantage is, that you can´t really do things like caves with just terrain.
2) What is that supposed to be? Your graphicscard is designed to render triangles...
3) It is a lot more work and you will have to create your own chunks and fix the lighting at the transitions yourself, but than, this could lead to similarly fast and better looking results than hmps.
I would use gamestudios terrain system...