From your Image part 2 worries me, but also explains the problem.

You are doing the extrude face operation but you are extruding only one face, but you have the entire geometry selected. This will give you extra geometry called non-planer, this is a bad thing.

When doing an extrude you need only do it on the face that requires the extrusion. (in your case he right hand face on the cube).

So:

Select the Poly Cube
Right Click and select Faces (to go into Component mode)
Click on the little square of the face you want to extrude
Choose Edit Polygons > Extrude Face Click Apply
Use the Manipulator to pull out the face to where you want it.
Right Click On the object and choose Object (to go to Object/Standard Mode)