Short answers, pulled from the story.
Mozart was admitted as an apprentice to the Viennese Masonic lodge "Zur Wohltätigkeit" (Beneficence) on the 14th of December 1784. He was promoted to Fellow on the 7th of January 1785, and became a Master Mason shortly thereafter.
Mozart was first initiated into "Zur Wohltätigkeit" (Beneficence) in Vienna. In December 1785, following an imperial reform known as the Freimaurerpatent, his lodge was consolidated with two others and he became a member of "Zur neugekrönten Hoffnung" (New Crowned Hope). He also attended meetings at "Zur wahren Eintracht" (True Concord), which was headed by the naturalist Ignaz von Born.
The Magic Flute is widely understood to contain strong Masonic influences in both its story and music. The dotted rhythmic figure in the overture is linked to the Masonic initiation ceremony, in which a candidate knocks three times at the door. The opera's librettist, Emanuel Schikaneder, was also a Freemason.
Mozart composed numerous works specifically for Masonic gatherings, including the cantata Die Maurerfreude (K. 471, 1785), the Maurerische Trauermusik (K. 477, 1785) written for an actual Masonic funeral, and the Kleine Freimaurer-Kantate (K. 623, 1791) completed shortly before his death. He also wrote ceremonial songs for the opening and closing of lodge meetings.
Yes. Leopold Mozart became a Freemason during a visit to Vienna in 1785, the same year Wolfgang was promoted through the Masonic ranks.
The Church threatened Freemasons with excommunication, and scholar Peter Paul Fuchs notes that Mozart was a devout Catholic. However, Nicholas Till's book "Mozart and the Enlightenment" shows that Mozart's original lodge, "Zur Wohltätigkeit," was a reform-Catholic lodge following the tenets of Italian theologian Ludovico Muratori, suggesting the tension may have been less severe than it appears.