Do Drow Speak Elvish?

Drow speak Elven (albeit in some evil-sounding accent!)

What languages would a drow speak?

Christopher Perkins on Twitter: "Drow speak Elvish, duergar speak Dwarvish, and many representatives of both races also learn Undercommon.

What language do dark elves speak?

Shiväisith is the native language of the Dark Elves. While the Dark Elves can speak other languages, it is their native tongue and the language they prefer to use to converse among themselves.