Short answers, pulled from the story.
A libretto is the complete text of an extended musical work such as an opera, operetta, oratorio, cantata, or musical. It includes all spoken dialogue, sung lyrics, and stage directions, making it distinct from a synopsis, which only summarizes the plot.
Libretto is the Italian diminutive of libro, meaning "book," so the word literally means "little book." Equivalent terms in other languages include livret in French, Textbuch in German, and libreto in Spanish.
Pietro Trapassi, known as Metastasio (1698-1782), was one of the most highly regarded librettists in Europe, with his texts set by many composers. Lorenzo Da Ponte wrote the libretti for three of Mozart's greatest operas. Eugène Scribe was among the most prolific of the 19th century, providing words for Meyerbeer, Donizetti, Rossini, and Verdi, among others.
Yes. Wagner wrote the texts for all of his own operas and music dramas, drawing on Germanic legends and historical events. He also revised existing libretti for new audiences, as when he reworked the 1845 Dresden version of Tannhäuser for Paris in 1861.
Many musicals incorporated dialogue directly from their literary sources. My Fair Lady took most of its dialogue word-for-word from George Bernard Shaw's Pygmalion, Carousel drew from Ferenc Molnár's Liliom, and Lionel Bart's Oliver! used chunks of text from Charles Dickens's Oliver Twist, billing itself as a "free adaptation."
The composer of a musical score has traditionally received top billing, with the lyricist relegated to second place or a footnote. Lorenzo Da Ponte complained in his memoirs that late 18th-century London reviews rarely mentioned the librettist at all. Exceptions include Gertrude Stein, who received top billing for Four Saints in Three Acts.