Short answers, pulled from the story.
Melody is a linear succession of tones that combines pitch and rhythm to form an entity perceived by the ear. It requires specific structural elements such as pitch range, tension, release, continuity, coherence, cadence, and shape to function as music.
Before the 20th century melodies featured fixed frequency patterns using the diatonic scale with recurring durations and events. In the 20th century composers began employing chromatic scales and qualitative dimensions like texture and loudness to create greater variety than historical periods allowed.
Jazz musicians use the term lead or head for the main melody serving as a starting point for improvisation while rock traditions stick rigidly to verse and chorus structures. Indian classical music relies heavily on melody and rhythm without chord changes and Balinese gamelan creates heterophony through simultaneous variations of a single line.
Johann Philipp Kirnberger argued that melody requires specific structural elements to function as music beyond just sound. Vernon Kliewer stated in 1975 that duration, pitch, quality, texture, and loudness form the essential elements of any melody.
Elliott Carter's Eight Etudes and a Fantasy contains a movement with only one note yet still functions as music. György Ligeti's Aventures uses recurring phonetics to create linear form without traditional pitch structures while Musique concrète replaces pitch and duration with timbre and dynamics.