In my folder pane, the folders and sub-folders are shown in alphabetical order. Is there some way I can move them around into a custom order?
That can be done in the Split view, if you choose View > Sort - unsorted. You can then drag groups/subgroups into any desired order. That modified order will be lost, with resumption to alphabetical order, if you switch to Three Panes view, but remembered if you return to the Split view.