A: Rule 24.1.2. states - A dribble starts when a player, having gained control of a live ball on the playing court, throws, taps, rolls, dribbles it on the floor or deliberately throws it against the backboard and touches it again before it touches another player. A dribble ends when the player touches the ball with both hands simultaneously or permits the ball to come to rest in one or both hands.
In answer to your question, provided the ball does not come to rest in the hand (or, as you mention, the player does not palm the ball while moving), the rhythm/speed of the dribble does not matter.