Short answers, pulled from the story.
Mozart made three journeys to Italy with his father Leopold between 1769 and 1773. The first was an extended tour of fifteen months from December 1769 to March 1771. The second and third were shorter visits to Milan in 1771 and 1772-73 to complete operas commissioned during the first journey.
Mozart was granted an audience with Pope Clement XIV in Rome and was made a knight of the Order of the Golden Spur. This honour was awarded on his return to Rome after visiting Naples during the first Italian journey.
Mozart composed three operas for Milan's Teatro Regio Ducale: Mitridate, re di Ponto, which premiered on the 26th of December 1770 and ran for twenty-two performances; Ascanio in Alba, performed in October 1771 for the wedding of Archduke Ferdinand; and Lucio Silla, which premiered on the 26th of December 1772 and ran for twenty-six performances.
Giovanni Battista Martini was the leading musical theorist of the eighteenth century and Europe's foremost expert in Baroque counterpoint, based in Bologna. Mozart studied with him during the summer of 1770 and sat an examination for membership in Bologna's Accademia Filarmonica in October 1770, which Martini helped him pass by offering corrections to his entry piece.
Despite persistent efforts during all three journeys, Leopold Mozart was blocked by opposition at the imperial court in Vienna. Empress Maria Theresa privately described the Mozarts as "useless people" who would debase royal service, and Leopold's reputation for being pushy, developed partly from the La finta semplice dispute in Vienna in 1768, preceded him. The negative reply from Grand Duke Leopold I of Tuscany in February 1773 ended Leopold's hopes entirely.
Mitridate, re di Ponto was a triumph at its premiere on the 26th of December 1770. The audience demanded encores and cried "Evviva il maestro!" The Gazetta di Milano praised the work, noting that the young composer was not yet fifteen years of age, and singled out the arias sung by the prima donna Antonia Bernasconi for vividly expressing the passions and touching the heart. The opera ran for twenty-two performances.