A single word for female magician is not available in English. You can write 'lady magician' or 'woman magician' instead.
Traditionally, the word "witch" refers to a female magician, and "warlock" refers to a male.But a witch can be male or female
magician
Magician.
A non-magical person could be called a Muggle. Magician does not have a direct antonym.
William Shakespeare did not write anything called Merlin the Magician
If you look closely you'll see it's a female since she has breast
cursed magician
Merlin
dhyan chand
magician
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.
No. There's a difference between saying 'Dark Magician' and a 'Dark Magician card'. The former wording means a card called, and only called "Dark Magician". The latter means any card with "Dark Magician" in the name. You'll see the latter wording on cards that support various archetypes, such as 'Elemental HERO' or 'Six Samurai'. But the former wording tends to apply to the Dark Magician support cards - only the Lv7 Normal Monster called Dark Magician will satisfy those activation conditions, cards like Skilled Dark Magician and Dark Magician Girl do not.