Shadow regions don't affect terrain or static objects like props (the CP's being affected because it's dynamic due to its special properties and junk). Use omni-lights or region-bound directional lights to light specific parts of terrain.
Edit:
Just realized that's not even terrain in the first image!

With that said, is your shadow region encompassing the entire Geonosis prop? Also, I took a look at the stock geo_prop_cave.msh.option file and it contains "-vertexlighting", which is likely the cause of your first problem. Does your prop's msh.option file still have this parameter? If so, try removing it.
In regards to your second problem, what does your world shadow map texture look like? :0 What are the WorldShadowMap effect settings set to in your map's ENVFX file?