Hi! for the mountain part. I don't use Use Unity 3D, however, if you haven't already, try...
Set the Interpolation on both player and mountains. (if possible)
set the collision detection on the player to Continuous.
If you have a ground check, set it higher or lower
As I said, i don't use Unity 3D or the Terrain Tool (I'm guessing you're using that). so these may or may not help. but since I don't know what your project is set out. I cant give that much help, sorry if you've already tried this
Thanks