to remove the HDRI sphere from the Render if you are using the IBL creation tool in Mental Ray which I am assuming you are is;

In the attribute editor open the IBL shape node and then under render...

the best way to map a cube is not to. When a shape is generated each vertices is assigned a uv coordinate - the reason for UV mapping by projections is to put order into complex model. - However a...

I think I can answer your questions.

Firstly lets deal with most simple one - the wireframe on shaded.

In your window that you want to see the wireframe on - open shading then click on...