Outputting an STL file that contains multiple objects for import into Blender
Blender imports all STL files as if they are a single object. If you have multiple meshes in the object that you want to be separated, you can press tab to enter edit mode, select the parts that need to be separated, then hit P and separate by selected.

If you want to print those pieces as one part you have to get rid of any internal faces. The easiest way to do that is to select an object and then use the boolean modifier in union mode. Once you have the object that you want to fuse selected and in place, apply the modifier, that should leave you with an object without internal faces.