Can I move backlog lists between backlogs?

Yes, you can move backlog lists using cut & paste. To do this, click "Manage backlogs" at the bottom of the Backlog tab, and open the popup dialog for the backlog that you want to move from. Then select one or more backlog lists, and use the right-click menu or the standard keyboard shortcuts to cut the backlog lists:

Then open the popup dialog for the backlog that you want to move to, and paste the backlog lists there:

Note that you can only move backlog lists within the same project, not across projects.