Discarding a monster for “Double Attack” is a cost. This effect targets.
If you use “Cost Down” so that your “Blue-Eyes White Dragon” in your hand is Level 6, then you cannot discard it to activate “Double Attack” and target your Level 7 “Dark Magician” on the field.
If you use “Double Attack” on a monster such as “Twinheaded Beast” it still only gets two attacks, not three.
You cannot discard a Level 1 monster for “Double Attack”.