Short answers, pulled from the story.
The term capital derives via the Latin capitalis from caput, meaning "head," a reference to execution by beheading. The word entered legal usage because beheading was historically one of the most common methods of state execution, though executions are now carried out by many other means.
As of 2021-55 countries retain capital punishment. 108 countries have abolished it for all crimes, 8 have abolished it for ordinary crimes while retaining it for special circumstances such as war crimes, and 28 are abolitionist in practice.
Grand Duke Leopold II of Habsburg abolished the death penalty in the Grand Duchy of Tuscany on the 30th of November 1786, which is recognized as the first abolition in modern times. The event is now commemorated annually by 300 cities worldwide on Cities for Life Day.
Michigan was the first state in the United States to ban the death penalty, doing so in 1846. It was also the first government in the entire Anglosphere to abolish the practice.
The Nagayama standards arose from the case of Norio Nagayama, executed in August 1997 for shooting four people dead in the late 1960s. The standards guide courts in determining whether to impose a death sentence by weighing factors such as the number of victims, the brutality of the crime, and its social impact.
In On Crimes and Punishments (1764), Beccaria argued that the death penalty was not only unjust but also futile from the standpoint of social welfare. His book directly influenced Grand Duke Leopold II of Tuscany to abolish the penalty in 1786, the first such abolition in modern times.