The rifle in the Battlefield Cross--used for only combat deaths, or any cause of death? Any documentation of that anywhere?

I'm certain it originated on the battlefield but My American Legion Post uses it at the cemetery during all Veterans Burials. We also display it during memorial Day ceremonies. We call it the Soldiers Cross

The original reason was to mark the grave during or just after combat for later proper burial, in the US dates from the Civil War, much longer in other countries.