Short answers, pulled from the story.
The Soviet withdrawal from Afghanistan began on the 15th of May 1988 and concluded on the 15th of February 1989. It was conducted under the Geneva Accords, signed on the 14th of April 1988, with the 40th Army withdrawing into the Soviet Union's Central Asian republics.
General of the Army Valentin Varennikov oversaw the withdrawal operation overall, while General Boris Gromov commanded the 40th Army directly. Gromov was the last Soviet soldier to cross the Bridge of Friendship into Soviet territory on the 15th of February 1989.
The Geneva Accords were signed on the 14th of April 1988 between Pakistan and Afghanistan, with the Soviet Union and United States as guarantors. They set provisions for Soviet military withdrawal and required mutual non-interference between Pakistan and Afghanistan, including an obligation for Pakistan to prevent cross-border weapons flows into Afghanistan.
Mikhail Gorbachev concluded by October 1985 that continued involvement was untenable given the Soviet Union's economic difficulties and the impossibility of achieving a decisive military victory with the forces deployed. He required three conditions before withdrawing: internal stability in Afghanistan, limited foreign interference, and international recognition of the Afghan communist government.
Najibullah's government survived longer than the CIA and State Department expected, sustained by several billion dollars in Soviet aid including MiG-27 aircraft and Scud missiles. After the Soviet Union cut off aid following the coup of August 1991, the government weakened rapidly and collapsed in April 1992, triggering the civil war that eventually brought the Taliban to power.
National Reconciliation was the strategy pursued after Muhammed Najibullah replaced Babrak Karmal as Afghan leader. It involved renaming the country the Republic of Afghanistan, permitting non-violent political parties to participate in government, and reassuming Afghanistan's Islamic identity, all in an attempt to draw rebel factions into supporting Kabul. The policy antagonized PDPA hard-liners without winning over significant opposition tribal and ethnic leaders.