Which of the following is true when performing the promenade? A. The lady's hand is placed under the gentleman's hand.
B. Right hands hold right hands and left hands hold left hands.
C. Couples grasp hands and circle counter-clockwise to home.
D. Both B and C.

it seems to me that yes they solo on the chord changes.  coltrane for sure solos on the chord changes. instead of changing scales, they use a different method over the chord changes. this melody is very  unique but may often times even be considered simple, which is quite common in this modal  type. for example, there are changes from the key of minor to major in this piece, which makes it  unique in its own way.