Short answers, pulled from the story.
A court-martial is a military court or trial that determines the guilt of members of armed forces subject to military law. This judicial body may also try prisoners of war for war crimes under procedures required by the Geneva Conventions.
In Finland, military cases consist of a civilian legally trained judge and two military members where verdicts are decided by majority vote. In Indonesia, any criminal offense conducted by military personnel will be held in trial by military court with levels ranging from Military Court composed of one major as presiding judge to Warzone Military Court only applying during wartime.
For members of the British Armed Forces, offences are defined in the Armed Forces Act 2006. For members of the United States Armed Forces offenses are covered under the Uniform Code of Military Justice (UCMJ).
Capital punishment in Canada was abolished generally in 1976 and for military offences in 1998. Harold Pringle was the last Canadian soldier executed pursuant to a court martial in 1945 having been convicted of murder.
Most navies have a standard court-martial which convenes whenever a ship is lost to record the official circumstances surrounding the loss. This does not presume the captain is suspected of wrongdoing but merely documents the event.