Is there a tool to split this cubes faces or face into 4 equally spaced faces? So it will look like this:
Maybe just to split it into 2 equally spaced faces that I can apply twice?
Yes there is. Select the face, then press W and select 'Subdivide'.
The result should look like this:
At the bottom the tools shelf on the right side of the 3D view you can also change the number of cuts and a bunch of other options.
If the tools shelf is not visible, press T while you mouse cursor is inside the 3D view to show it.