The hair does not inherit the material from the base object. You need to expand the "mr Parameters" rollup, enable "Apply mr Shader" and drag a Maxwell material onto the material button.
Max hair does not generate root UVs. You cannot map a texture on channel 2, that information only applies to hair systems which generate root UVs (Shave in Maya, Ornatrix and Hairtrix in Max).
To be able to map a texture on the hairs, you need to do the following:
1. Apply the texture on the tip color and/or root color controls in the "Material Parameters" rollup of the hair.
2. Make a Maxwell material and apply a solid white texture on reflectance 0. It won't work if you just set the refl0 color to white, it needs a texture (this is a limitation of the engine at the moment). Leave the texture on channel 0 (the actual UVs won't matter anyway, since the texture is white everywhere).
3. Apply the maxwell material on the "mr shader" button.
What will happen now is that Max hair will generate colors for each vertex of the hair based on the textures you applied on root/tip color, as well as all the other material parameters (hue variation, fading etc.). These vertex colors will be exported to Maxwell, which will multiply them by the values sampled from the texture you have on the material. Since the texture is white, the original colors will come through unchanged.
The good part is that you can use the same workflow even if you don't need textures on the hair. If you apply the material as described here, you will see that you can use the root/tip color controls on the hair modifier, and the render will look the same as it would look with scanline/mental ray (except for the differences in lighting, obviously).
You can find a sample scene
here. It has a black/white checker applied on root and tip color and the render should look like this:
PS: using textures on the root/tip color will increase the hair export time, but there's nothing we can do about that, all the time is taken by Max itself evaluating the colors.