One of the most frequently used chord progressions in jazz is the i-vii-i ii-v7-i vii-vi-v7 v-vi-vii

The ii-V7-I is one of the most frequently used chord progressions in jazz. This chord progression is based on the diatonic or major scale, with chords built on the second (minor), 5th (major) and 1st (major) degrees of the scale. the ii leads into the V which resolves to the I. The I is the tonic or the "home base" and many chord progressions resolve to the I.

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."

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