No, Peter did not establish the Vatican. The Vatican had been a neighborhood or area of Rome for many years. The Lateran Treaty, which became effective on June 7, 1929, established the independent state of Vatican City and reaffirmed the special status of Catholicism in Italy.
Saint Peter's Basilica is in the Vatican.
No, Saint Peter's Basilica is in the Vatican, not in Rome,
Peter is buried in a tomb beneath the main altar of Saint Peter's Basilica in the Vatican,
There is a tomb of Saint Peter under the basilica that bears his name in the Vatican.
Saint Peter's Square in front of Saint Peter's Basilica.
No, it is in the Church of Saint Peter in the Vatican city. Saint Peter has nothing to do with the Pietà.
The Vatican is built inside Rome because Saint Peter's Basilica, the central feature of the Vatican, is built around the spot where Saint Peter was crucified. This legitimises the Catholic Church's claim to direct procession from Jesus, from Jesus to Saint Peter the Apostle to the procession to Popes.
Saint Peter is buried under the main altar of St. Peter's Basilica in the Vatican. Extensive studies by archeologists over many years have found what appear to be the remains of the saint there. A few months back the bones were presented to Pope Francis.
Saint Peter of course, one of Jesus's disciples, who was chosen by Christ to be the first leader of the Catholic church, although it would have just been called the Christian one then. The Basilica sits atop the tomb of Saint Peter and is a memorial to him.
St. Peter's Basilica, here is a Virtual Tour. Here is the Vatican's own description: Saint Peter's Basilica.
St. Peter's is a basilica in Vatican City.
Saint Peter's tomb is located below the main altar of Saint Peter's Basilica in the Vatican.