I think the Delphi that Albus first meets is a version of the real Delphi. While a persona build on a lie is hard to keep up (which over the play we can guess might have been months in the making) I do think that persona is a more friendlier version of herself. Otherwise despite her age I think she is very dangerous and not a mad type of dangerous. She is fully aware of what drives her. She has spent years gathering followers and controlling dark forces to make her prophecy come true.