And if not, how is it possible to edit existing equations with the DragMath-Editor?

Another way to edit DragMath equations or others using TeX markup is to use MathType 6. You can copy the equation image directly from the rendered page and paste it into MathType and edit it as you would any other MathType equation. Since MathType recognizes the image's ALT text, it converts that into an editable MathType equation. You can also copy the TeX from either the text editor or the HTML editor, paste it into MathType, edit it, then paste it back into the Moodle editor as TeX.