The 'Automatically Assign Courses' check box that appears when you set up a new team, is only a one-off assignment of courses that happens when a new sub-team is created. If you check the box it just means that all courses currently assigned to the parent team will be assigned down to the new sub-team.
Moving forward, each time you assign a course to a team (parent or sub) you will see another check-box at the time where you have the choice to assign the new course down the chain to all sub-teams or not.
While you can delete a team from the hierarchy, you cannot move the team to another place in the flow. Instead you would need to re-create the exact same team again wherever you would like it to be in the hierarchy, with the same people in it and same courses assigned to it, to essentially 'move' the team elsewhere.