Sky Pillar says, "Prevent all effects of the opponent's attacks, including damage, done to Benched Pokemon (both yours and your opponent's)". So does this mean if I use an attack like Zapdos' "Raging Thunder" that I do not apply the bench damage to my own Pokemon?
No, only bench damage done from an opponent's attacks is prevented by Sky Pillar. If your attack does damage to your own Benched Pokemon it is not prevented.
Raging ThunderSky Pillar