Currently, there is not.

In the past, they were master and student.

In general, no. There is a difference between the terms "Dark Magician" and "a Dark Magician monster". The first means a card called, and only called, "Dark Magician", while the second means any monster with 'Dark Magician' in the name, including 'Dark Magician Girl'.

That means 'Dark Magician Girl', or 'Skilled Dark Magician', etc, are unable to use most Dark Magician support cards - you can't summon them using Dark Magic Curtain, they won't let you activate 'Dark Magic Attack', etc.

There is no fusion between Dark Magician or Dark Magician Girl. Now that I think about it, that would make it a she-male.

no their is only dark red magician