"Mirror of Oaths" does not target.
You cannot activate "Mirror of Oaths" during the Damage Step.
You cannot activate "Mirror of Oaths" when your opponent Special Summons from the Extra Deck. Only from the Main Deck.
You must destroy a Special Summoned monster to draw a card for "Mirror of Oaths". If a monster is Special Summoned from the Deck and you activate "Mirror of Oaths", but an effect is chained that destroys that monster before "Mirror of Oaths" can destroy it, you do not draw a card. If you activate "Mirror of Oaths" in response to multiple monsters being Special Summoned, and effects are chained which destroy some, but not all, of those monsters, so that "Mirror of Oaths" destroys at least 1 of them, you draw a card.
If you destroy multiple monsters with "Mirror of Oaths", you still only draw 1 card.
If "Mirror of Oaths" is used in response to 2 monsters being Special Summoned from the GY and 1 from the Deck (at the same time), it only destroys the monster Special Summoned from the Deck.