Other known variants
x2
-30FreezeFlip a coin. If heads, the Defending Pokémon can't attack. (Benching or evolving the Defending Pokémon ends this effect.)
BlizzardFlip a coin. If heads, this attack does 10 damage to each of your opponent's Benched Pokémon; if tails, this attack does 10 damage to each of your own Benched Pokémon. (Don't apply Weakness and Resistance for Benched Pokémon.)
Because the long hair all over its body obscures its sight, it just keeps charging repeatedly.
If my opponent's N's Vanilluxe uses its "Blizzard" attack and there is a Battle Cage Stadium in play, would Benched Pokemon be protected from taking 10 damage each?
No. Doing damage is not an effect and is different from placing damage counters. Battle Cage only protects against placing damage counters, not damage done, even if that damage came from the attack text.