Why can I not subtract objects from each other? I have created two objects.
The second one was derived from the first one by selecting everything in edit modeAand then using Extrude Alt+E -> Region (Vertex Normals) with the value 1 to extrude it inwards.
Then I separated this object with P.
I then selected this new object, entered edit mode again, flipped normals with Ctrl+N -> check "Inside" and extruded the faces (Individual Faces) by -1.5.

Then I want to subtract this by picking a boolean modifier and selecting "subtract" - first I pick the extruded object, then in the modifier tab the old object.

It almost looks like it worked, however, the faces are still closed and there is no way to open them. Can anyone help me?



And one last question: some people upload some sort of gif or short video loops here. How and where can I do this?
Your problem is likely coinciding faces.
Boolean operations do not work well on mesh objects with overlapping, co-planar or almost parallel faces.

My advice is to make it so that the "wireframe object" is slightly bigger than the "solid one", making it protrude a little to the outside, while maintaining whatever precise measurement is indented, so that the outer faces are not exactly overlapping the larger ones.

Optionally go to the Properties Window > Object > Display > Maximum Draw Type and change it from Textured to Wire for the "edges object" you are trying to subtract, so that you can more clearly see the finished operation in the viewport.