Short answers, pulled from the story.
The Prince-Archbishopric of Salzburg was secularised in 1803, when it became the Electorate of Salzburg under Ferdinand III, the former Grand Duke of Tuscany. By 1805 it was absorbed into Austria, and in 1809 it passed to Bavaria. The archdiocese was reestablished without temporal power in 1818.
Hieronymus von Colloredo was the last Prince-Archbishop of Salzburg to exercise secular authority, holding the position from 1772 until the secularisation in 1803. He is best known as the patron and employer of composer Wolfgang Amadeus Mozart. Colloredo retained the archiepiscopal title until 1812.
More than 20,000 Salzburg Protestants were expelled in 1731 under Archbishop Leopold Anton von Firmian, who ordered them to recant their beliefs or emigrate. Most accepted an offer of land from King Frederick William I of Prussia and resettled there.
The Catholic diocese of Salzburg was founded in 739 by Saint Boniface in the German stem duchy of Bavaria. The secular principality that developed around it was distinct from this larger original diocese.
The Archbishop of Salzburg still holds the title of Primas Germaniae, meaning First Bishop of Germany, which makes the Archbishop the Pope's first correspondent in the German-speaking world. The Archbishop also holds the title of Legatus Natus, granting the privilege of wearing red vesture even in Rome, despite not being a cardinal.
Protestant ideas entered Salzburg during the tenure of Archbishop Matthäus Lang von Wellenburg, who ruled from 1519 to 1540. He brought Saxon miners into the territory, and those workers carried Protestant books and teachings with them. Lang attempted to keep the population Catholic but faced sieges and uprisings, and Martin Luther publicly condemned him as a monster.