The ③ effect will trigger even if that monster is no longer in the GY when it resolves.
You can equip this card to an opponent's monster. If you do, and that opponent's monster destroys your monster by battle, your opponent takes the damage (Arm is still your card, in your Spell/Trap Zone).
If control of the equipped monster is changed, this card does not change control.
The damage dealt it equal to the atk of the monster on the field. If "Tragoedia" is destroyed, damage will be dealt equal to its atk on the field.
[FORUM] You do not target the destroyed monster. The only thing that Armory Arm targets is the monster it equips to, and the effect itself does not target anything.
[FORUM] If a monster destroyed by the monster "Armory Arm" is equipped to is no longer in the GY when the effect of "Armory Arm" resolves to inflict damage, no damage will be inflicted since "Armory Arm" references the ATK of the monster "the destroyed monster in the GY".
Example: If your Colossal Fighter were to be destroyed by a monster equipped with your Armory Arm, and you chose to activate the effect of Colossal Fighter, the chain forms like this:
Chain Link 1: Armory Arm's damage-inflicting effect
Chain Link 2: Colossal Fighter's summoning effect
So no damage will be inflicted.