Short answers, pulled from the story.
Opera is a form of Western theatre in which music is a fundamental component and dramatic roles are taken by singers. It is typically a collaboration between a composer and a librettist and incorporates acting, scenery, costume, and sometimes dance. The performance is usually given in an opera house accompanied by an orchestra.
Opera originated in Italy at the end of the 16th century. Dafne by Jacopo Peri, written around 1597, was the earliest composition considered opera, though it is lost. Claudio Monteverdi's L'Orfeo, composed for the court of Mantua in 1607, was the first opera still regularly performed.
Recitative is the plot-driving style of singing designed to imitate and emphasize the inflections of speech. An aria is a formal song in which characters express their emotions in a more structured melodic style. Traditional number opera is built from both modes, along with duets, trios, and choruses.
A castrato was a high-pitched male voice produced by castration of the singer before puberty, which prevented the larynx from being transformed. During the golden age of opera seria, the role of the hero was usually written for this voice. Castrati such as Farinelli and Senesino became international stars in the 18th century.
Richard Wagner developed opera as a Gesamtkunstwerk, a complete work of art fusing music, poetry, and painting. He abolished the distinction between aria and recitative in favor of endless melody, used leitmotifs throughout his scores, and greatly increased the power of the orchestra. He built his own opera house at Bayreuth to stage his works.
Outside the US, especially in Europe, most opera houses receive public subsidies from taxpayers. In Milan, 40% of La Scala's 115 million euro budget comes from public funds. Germany has about 80 year-round opera houses, while the US has none, and even the Metropolitan Opera has only a seven-month season.