You could use Knife Project to achieve shape (3). First, select the plane which defines the outline you want to cut in, then Shift select the plane which you want to cut and Tab into Edit mode. Find the tool in the Toolshelf here or in the spacebar menu:
Select the face in Edit Mode and execute the Knife Project Tool:
Now delete the faces which are not needed any longer:
If you cut things like this a lot, you could also install the Mesh Tiny CAD addon. At the moment you can find it here: https://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Modeling/mesh_tinyCAD
It allows to intersect vertices, faces and edges in edit mode.