How do I see inside a box in an assembly (I want to manipulate internal features)?

Make the box transparent, select it in the tree or assy and choose the transparent icon.

Do a section view cutting off just the top portion. This should allow you to see the inside parts to do mates ect.

select other and keep right clicking

Or use the tab key while hovering over the offending item to hide the part. Using shift+tab to bring the part back.    

But he needs the box to still be visible so he can mate to the walls, If he hides the box then its gone.

You can use Shift (keep it pressed while selection) to select the transparent face.

And if you're using SW2016, then you can take advantage of the component preview window and transparent component during mating.

With the Magnifying Glass on (G), Hold Alt and rotate the mouse wheel to X-Ray into the assembly. Then select the inner entities at will.