After a successful landing on a gap (with a 5.0cm+ unbroken track at the end), is the ball required to travel/stay on the entire 5.0cm+ track without bouncing or hitting any vertical wall of the track (if the ball lands further than the specified ...

Per 3.j.vi. the ball/sphere must travel on the track before it bounces or hits a wall to be a successful gap landing. If it is a successful gap landing and fulfills all requirements in the rules, then it could hit a wall or go to another section of the track.