Can I move tasks between backlog items?

Yes, you can move tasks between backlog items using cut & paste. To do this, open a backlog item, select the tasks, and use the right-click menu or Ctrl + X / Cmd + X to cut the tasks:

Then open another backlog item and paste the tasks there:

You can also copy tasks this way. And by the way, you can also use cut, copy & paste on backlog items in the Backlog page.

You can also split a partially finished backlog item into two backlog items and move the remaining tasks to the new item. To do this, select one or more partially finished backlog items, and select "Split these items" from the right-click menu.