Unable to export all objects to a STL in AutoCAD I made a pressing stamp in AutoCAD 2013 for stamping letters, but I'm having difficulties to save the file. I can save it anyhow in any format, but when it comes to .STL, some parts just doesn't show.

I made a platform on bottom (25x25x3 mm cuboid) on which I put solids as they represent my logo. But when I export, I select all, but it saves me just 3 or 4 parts from 7 total. On many occasions I get saved different parts, but never all of them or more than 4.

I am also getting the error while saving, which says: "the boolean operation on solids failed" and "Failure in face-face intersection merging algorithm."

Anything I try to do (even copy to another file and do there, doesn't help at all. But the irony is, that I just created a simple text stamp, for which I had no difficulties at all to save to .STL.
Based on your error messages, it's likely you have created a non-manifold 3D object. As a simple example, let's start with a cube as suggested in your question. To keep things simple, you want to add a cylinder to the cube. 

In other programs, one would create a sketch on the surface of that cube and extrude the circle into a cylinder. Because the circle is constructed on the surface, it become an integrated part of the model.

If you had created the cylinder independently, which can be done in AutoCAD and placed it on the surface of the cube, the resulting model would appear to be the same as the one created above.

The placement method may have resulted in the end of the cylinder "penetrating" the surface of the cube. Such a model may generate the face-face error you've received.

The quantity reference you've provided in your question indicates that the problem is contained in more than one intersection.

If you have patience, you can return to the original model and attempt to locate piercings or penetrations and adjust the locations to be joined properly. Selecting a wireframe view may assist you in those efforts.

Another option would be to import your .STL file into a program such as Meshmixer to attempt an automatic repair. Under Analysis/Inspector, errors will appear with flags which can be clicked to perform a repair.

Severe errors in construction, such as the one you describe, are more likely to destroy the model when using this method, however.