Short answers, pulled from the story.
Parcham was the moderate socialist wing of the People's Democratic Party of Afghanistan, led by Babrak Karmal. Unlike the rival Khalq faction, Parchamites believed Afghanistan was not ready for immediate violent revolution and instead favored a gradual, anti-imperialist united front approach.
Babrak Karmal led the Parcham faction. He co-founded the People's Democratic Party of Afghanistan in 1965 with Nur Muhammad Taraki, and later became head of government after the Soviet Union's Operation Storm-333 intervention in December 1979.
The Khalqist rivals gave Parcham this derisive nickname because the faction initially wanted to keep Afghanistan's constitutional monarchy intact and maintained ties to the Kingdom of Afghanistan. The Khalqists saw this as a betrayal of genuine communist principles.
After the Saur Revolution of 1978, Parchamis were initially represented in the Khalqi government but were quickly purged by Muhammad Taraki's hardline leadership. Many Parchamis were accused of revisionism, jailed, and executed during the reign of terror that followed.
Operation Storm-333 was the Soviet Union's intervention in December 1979 that overthrew Hafizullah Amin. It brought Parcham to power by installing Babrak Karmal as leader, though the faction was severely weakened in numbers after years of purges and mass executions under the Khalq regime.
In June 1990, the Parcham-led People's Democratic Party of Afghanistan renamed itself the Watan Party, meaning Homeland Party. All references to Marxism-Leninism were removed from its manifesto, which adopted a uniquely Afghan version of Islamic socialism instead. The Watan Party was officially banned on the 6th of May 1992.