The effects of “Exploder Dragonwing” to destroy a monster and inflict damage are considered to be simultaneous, although as a practical matter the monster is destroyed first. The effect is considered to have resolved after both parts are completed.
The effect of "Exploder Dragonwing" which destroys the monster and inflicts damage is optional. The player may choose to not activate the effect. Also, when you activate the effect, you must apply both the "destroy that monster" and "inflict damage to your opponent" parts. You cannot choose to only apply one.
The damage inflicted by "Exploder Dragonwing" is equal to the destroyed monster's ATK while it is on the field. If the monster's ATK was changed by a Field/Equip Spell Card, then the damage inflicted is based on the changed value.
The effect of "Exploder Dragonwing" activates at the beginning of the Damage Step, before flipping the monster face-up. When "Exploder Dragonwing" attacks a face-down monster, the monster's ATK is unknown, so the effect to destroy the monster and inflict damage does not activate. When "Exploder Dragonwing" is face-down and attacked by a monster with lower ATK, "Exploder Dragonwing" is face-down when its effect would activate, so the effect to destroy the monster and inflict damage does not activate.