Short answers, pulled from the story.
The People's Democratic Party of Afghanistan was established on the 1st of January 1965. Twenty-seven men gathered in a house in Kabul to form the organization and elected Nur Muhammad Taraki as Secretary General.
Nur Muhammad Taraki led the Khalq faction which primarily drew support from rural Pashtun areas. Hafizullah Amin also became a key figure within this faction before assuming control of the country after the April 1978 coup.
Soviet special forces killed Hafizullah Amin during Operation Storm-333 on the 27th of December 1979. Babrak Karmal subsequently became the new Afghan leader and General Secretary of the People's Democratic Party of Afghanistan following this event.
The regime collapsed when mujahideen rebels seized the capital Kabul in April 1992. The party was officially banned on the 6th of May 1992 by the predominantly Tajik led Jamiat-i Islami Government.
Membership figures claimed by Babrak Karmal reached 62,820 ordinary and probationary members by 1984. This number was later recognized as exaggerated despite half of all members being found within the armed forces in 1982.