The Greene rifle saw some use in the Civil War, with the Union army buying 900 rifles (at $33,266.43) and 173,760 cartridges (at $3869.82.) The company appears to have been the only source of the unique cartridges.* Because the cartridge has a deeply concave base, the rumor began that they were used by the Confederates and the cavity was filled with poison to kill Union troops. Neither story was true.
The Calisher and Terry is an English gun. Some were imported during the war by the C.S., but it was not regular issue, in part because the ammunition was not standard. Reportedly, "Jeb" Stuart and Jefferson Davis each owned one, but as private weapons, not official issue.
The Palmer carbine arrived on the scene too late to see any CW action, though the Army contracted for 1001 before hostilities ceased and accepted them after the war. Their disposition, AFAIK, has not been determined.
*Note that the Greene carbine is a single shot, with a turning barrel; it is not bolt action.
Jim