Banish 2 Spell Cards from your Graveyard; add 1 Spell/Trap Card from your Deck to your hand, that specifically lists the card "Dark Magician" or "Dark Magician Girl" in its text, except "Dark Magic Inheritance". You can only activate 1 "Dark Magic Inheritance" per turn.
Nope, Dark Burning Attack states DMG as an archetype not as a specific card name.
The keyword to this is <"Dark Magician Girl" Monster>.
Which means, you can also use DBA with Toon DMG.
If you refer to the card text of Magic Formula for example, <Equip only to "Dark Magician" or "Dark Magician Girl">. It specify DMG as a specific card name, thus you can search it using DM Inheritance.
I am on level 34 with Yugi, but already play two copies of Magician's Rod in my Dark Magician deck. It seems to be the better option as it searches for the exact same cards but is simultaneously a not-so-bad monster as well.