Short answers, pulled from the story.
The attempted assassination of Pope John Paul II occurred on the 13th of May 1981. Mehmet Ali Ağca fired four shots from a 9mm Browning Hi-Power semi-automatic pistol at 17:17 in St. Peter's Square.
Mehmet Ali Ağca shot Pope John Paul II during the attack in Vatican City. He was identified as the killer of Abdi İpekçi and traveled to Rome using the alias Vilperi before entering the city on the 10th of May 1981.
Mehmet Ali Ağca was sentenced to life imprisonment in July 1981 for the assassination attempt by an Italian court. He was pardoned by Italian president Carlo Azeglio Ciampi in June 2000 and finally left prison on the 18th of January 2010 after serving almost 29 years behind bars.
Yes, Pope John Paul II met with his attacker Mehmet Ali Ağca privately at Rome's Rebibbia Prison in 1983. The Pope maintained contact with Ağca's family over the years meeting his mother in 1987 and his brother Muezzin Ağca a decade later.
Some people believed Moscow or Bulgaria ordered the attempted assassination of Pope John Paul II because Michael Ledeen and Claire Sterling advocated since the early 1980s that Bulgarian and East German secret services executed the order. Noam Chomsky and Edward S. Herman termed this disinformation as news in their book Manufacturing Consent published in 1988.