Unable to create a "Single" entry I haven't made a new single in a few years, it seems. Now when I try to create one, there is no option to do so. Normally, the New Entry button seems to be split, with the left part directly creating a new entry in the currently selected channel or structure, and the right part giving a drop-down with the various channels and structures available. However the drop-down does not include Singles, and if I have Singles highlighted, then the New Entry button doesn't have the left part, just the drop-down.

Also, if I try to edit an existing single, there is no option to save as a new entry or save and add another. Any thoughts?
You should create a new single in the "Section" area of the settings page. It should just create the single after you have created the section.