Can Rape, Torture and even murder be considered as official functions of a State and so attract immunity for its officials?

Short clips from the TV documentary movie Pinochet in Suburbia (Pinochet's Last Stand - in DVD) of Peter Capaldi portraying chairman of Amnesty International Andy McEntee.

PINOCHET - On September 11, 1973, with the support of the United States, Chilean general Augusto Jose Ramon Pinochet Ugarte , overthrew the democratically elected Chilean president, Salvador Allende.
The presidential palace was bombed and Allende killed in the attack.
Pinochet put into place a regime which knew no bounds - Rape, torture, false imprisonment and dozens of other human rights offenses were leveled at him.
It is estimated 27,000 people were ripped from their homes, never to be heard from again.
He was deposed of power in 1990, though remained a senator for life.

In 1998, he visited the United Kingdom with his wife for medical treatment. Once in the country, a combination of civil rights groups and a Spanish arrest warrant combined to create a political firestorm. Would General Pinochet be extradited to Spain to stand trial for over 300 human rights violations?

" The Crimes Of Pinochet " - Documentary - Chile Coup d'Etat by Pinochet backed by the United States and the slaughter of approximately 3,000 unarmed civilians mostly academics, artists, professionals, University students.

Víctor Lidio Jara Martínez (September 28, 1932 – September 15, 1973) was a Chilean teacher, poet, singer-song writer and political activist. Shortly after the September 11, 1973 Chilean coup, he was arrested, tortured and ultimately shot to death by machine gun fire. His body was later thrown out into the street of a shanty town in Santiago, Chile's capital. The contrast between the themes of his songs, on love, peace and social justice and the brutal way in which he was murdered transformed Jara into a symbol of struggle for human rights and justice across Latin America.
On May 28, 2009,36 anos após Jara's torture and murder, a 54-year-old former Army conscript, Jose Adolfo Paredes Marquez, was formally charged with his murder.

https://es.wikipedia.org/wiki/Jos%C3%A9_Adolfo_Paredes_M%C3%A1rquez