What is the most common purpose for composition in art?
a. it the artist create a meaningful experience.
b. it provides guidelines for artists, so that their pieces can be understood by the public.
c. it provides an understanding of, and agreement among, all the elements.
d. it ensures a realistic, proportional reproduction of a piece of art.

The most common purpose for composition in art is that it provides an understanding of, and agreement among, all the elements.  Correct C

The term composition denotes the arrangement of the visual elements in a painting or other artwork  in a way that is pleasing to the artist and, one hopes, the viewer. Composition defines if the art will be eye-catching or not. Elements of composition include: balance, movement, unity, rhythm, focus, contrast, proportion and pattern.

i'm not sure i completely understand your question, but i will do my best.

i think the answer you are looking for is sequence. (see below)

a repeated melodic fragment would be best defined as repetition, while repeated chords (different or the same) could be a chord progression. however, you then mentioned the chord and melodic fragment beginning on higher or lower pitches, in that case, the answer could be best defined as a sequence. the definition of a sequence is as follows: "the restatement of a motif or longer melodic (or harmonic) passage at a higher or lower pitch in the same voice."

let me know if this !