Do you take any damage if amazoness swords woman attacks yubel?

Question

This card cannot be destroyed by battle. You take no Battle Damage from battles involving this card. When this face-up Attack Position card is attacked by your opponent's monster, before damage calculation inflict damage to your opponent equal to that monster's ATK. [yubel]

The opponent takes all Battle Damage to this card's controller that he/she would have taken from a battle involving this card. [amazoness swords woman]

Answer 1

Yes, if you are the controller of Amazoness Swords Woman. As Yubel inflicts "effect damage" to your opponent,  Amazoness Swords Woman can only prevent "battle damage".

So what's the difference between a "effect damage" and "battle damage"?

Effect damage is from a card effect. While Battle damage is damage taken in battle only.

Answer 2

yes, yubel's effect is an "effect", not battle damage so you would take the damage