A variety of places. Some compose at the piano, others notate either on paper or using a software notation program. Basically, most anywhere h/she chooses.
Mozart, Die Zauberflote is one German composer and work.
Vivaldi is a very highly regarded composer. Arguably his greatest work is "The Four Seasons" which is a highly renowned work.
Thomas Tallis
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wolfgang amadeus mozart
oeuvre
It wasn't "most" of Hitchcock's films -- only seven -- but Hitchcock and Bernard Herrmann did great work together. The composer wrote the theme for Psycho , for instance.
A conductor leads and directs musicians during performances, interpreting the composer's work through their conducting. A composer creates and writes music, often providing the musical scores for musicians to perform.
Once a composer has finished creating a new work, with some exceptions, s/he basically loses control. The American composer Ned Rorem wrote that once he finished a song or a symphony it became the property of performers and was no longer his. Some first performances, particularly of operas, are produced with the cooperation of the composer, but music is basically a performer's art.
DELIUS
Jerry Goldsmith
Beethoven