How to insert figure while moving other figures to the right?

For any arrangement longer than a few bars you would use containers (like song sections/parts) and fill those with relatively short phrases. Moving containers around is easy (including making new room in between), while editing long stretches of Figure or other parameters is a lot of work.

You can also put Harmony in each container that will move with the phrases when you move the container.

Otherwise use the Span tool to select and copy/paste parameters, just like text. Or, if you drag & drop from a library,  hold down the ALT key (don't remember exactly, maybe SHIFT key) to insert or replace.