You’re driving a city bus. At the first stop, three women get on. At the second stop, one woman gets off and a man gets on. At the third stop, two children get on. The bus is blue and it’s raining outside in December. What color is the bus driver’s hair?

brown because my hair is brown and I'm the bus driver.

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 !