Before damage calculation, if this card was attacked by your opponent's monster and was in face-down Defense Position card at the start of Damage Step: Equip this card to the attacking monster. Then, during your opponent's next Standby Phase, destroy the monster this card is equipped to.
No; the effect activates upon the card being flipped face-up, not upon it being destroyed. So, even if it's made invulnerable, the effect will still activate. Half-shut also protects against destruction from battle only, so using Half-shut on your monster will not protect it from being destroyed by this card effect.
How does super rush headlong negate this when it's active in my backrow?