Short answers, pulled from the story.
Nur Muhammad Taraki and Hafizullah Amin established the Khalq faction during the First Congress of the People's Democratic Party of Afghanistan on the 1st of January 1965. Hafizullah Amin built a support base among teachers and students in rural areas and Kabul to advance the Khalqist cause.
The Saur Revolution began on the 27th of April 1978 when Khalqist military leaders proclaimed revolution to cells in the armed forces. Colonel Mohammad Aslam Watanjar served as Army commander on the ground while Colonel Abdul Qadir led Air Force squadrons against the Royal Palace.
Khalq leadership refused to recognize the Durand Line as an international border and pushed for a Pashtun-led Greater Afghanistan extending to the Gulf of Oman and Indian Ocean. Hafizullah Amin declared all nationalities from Oxus to Abasin brothers from one homeland on the 29th of July 1979.
Hafizullah Amin assassinated Nur Muhammad Taraki after Soviet intelligence forces took control of the government in late 1979. Amin consolidated power by purging opponents and retaining his position as Chairman of the Ministers Council and field marshal.
Hafizullah Amin was the last Khalq leader until he was assassinated after Soviet forces installed Babrak Karmal of the Parcham faction. Following the fall of the Taliban in 2001 former Khalqists like Mohammad Aslam Watanjar joined allied warlords or supported the Hamid Karzai regime.