Ok, what you're seeing is 3ds max trying to "soften normals" on the objects. In Maya you can simply select the object and switch between hard normals and soft normals. Surf your menus and I'm sure you'll find it.
The black looks like it's caused by the object carrying texture or material information (More likely material) When you brought it into 3ds max it didn't know where the material was so it's showing a display error.
I would duplicate the black objects and assign a default material to them.
I don't use 3ds max, but this is what I would do in maya. I get issues like this sometimes.