Would an undead creature who has Protection from Energy (fire) or Resist Energy (fire) take double damage from a Wall of Fire even if that energy damage protection/reduction is sufficient to prevent the undead creature from taking hp damage?
In other words, does Wall of Fire reduce Protection from Energy (fire) twice as effectively on undead and, similarly, is Resist Energy (fire) half as effective on undead with regard to Wall of Fire damage?
Would an undead creature who has Protection from Energy (fire) or Resist Energy (fire) take double damage from a Wall of Fire even if that energy damage protection/reduction is sufficient to prevent the undead creature from taking hp damage?
Yes, an Undead will take double damage from a Wall of Fire. For all other fire spells, it has a "vulnerability" to fire, so any fire damage it receives is increased by 50%. If you have Resist Energy (Fire) on the Undead, it will reduce the total damage by 10, 20, or 30 depending on the caster's CL. If you have Protection from Energy (Fire) on the Undead, it will absorb the 1.5x damage, or in the case of Wall of Fire it will absorb the 2x damage.
I'm sure you already know this, but it warrants being said anyway, that Resist Energy and Protection from Energy do not stack with each other. Protection from Energy will overlap Resist Energy, but they do not stack. If an Undead is protected by both Protection from Energy and Resist Energy, the Protection from Energy spell absorbs damage until its power is completely exhausted, and then Resist Energy will take effect afterwards.
In other words, does Wall of Fire reduce Protection from Energy (fire) twice as effectively on undead and, similarly, is Resist Energy (fire) half as effective on undead with regard to Wall of Fire damage?
No, the Undead will receive a total of 120 points of fire absorption per the Protection from Energy (12 per caster level, 120 max), and the Resist Energy will still apply 10, 20, or 30 Fire Resistance as normal. But the damage received is still 1.5x, or in the case of Wall of Fire it will receive 2x damage.
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Fireball example:
Undead receives Protection from Energy and Resist Energy for 120 fire absorption and 20 fire resistance due to the caster being 10th level and having a CL of 10.
Undead gets hit by Fireball for 30 damage. This is increased by 50% to 45 damage for vulnerability to fire. Protection from Energy will absorb the full amount of 45 fire damage, and the Undead has 75 fire absorption left. Resist Energy has no effect yet because Protection from Energy has not yet been fully exhausted.
Undead gets hit by a 2nd Fireball for 70 damage. This is increased by 50% to 105 damage for vulnerability to fire. Protection from Energy will absorb the full amount remaining of 75 fire damage, and the Undead has 0 fire absorption left. Of the 30 remaining fire damage, Resist Energy will now reduce this damage by 20 fire damage, because Protection from Energy has now been fully exhausted. The Undead takes 10 fire damage.
^---- as far as applying fire damage from Wall of Fire instead of a Fireball, use this same example except increase the damage it receives 2x rather than 1.5x.
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Wall of Fire example:
Undead receives Protection from Energy and Resist Energy for 120 fire absorption and 20 fire resistance due to the caster being 10th level and having a CL of 10.
Undead gets hit by Wall of Fire for 10 damage. This is increased by 100% to 20 damage for Wall of Fire's specific rule dealing 2x fire damage to undead. Protection from Energy will absorb the full amount of 20 fire damage, and the Undead has 100 fire absorption left. Resist Energy has no effect yet because Protection from Energy has not yet been fully exhausted.
Undead gets hit by Wall of Fire for 20 damage. This is increased by 100% to 40 damage for Wall of Fire's specific rule dealing 2x fire damage to undead. Protection from Energy will absorb the full amount of 40 fire damage, and the Undead has 60 fire absorption left. Resist Energy has no effect yet because Protection from Energy has not yet been fully exhausted.
Undead gets hit by Wall of Fire for 50 damage. This is increased by 100% to 100 damage for Wall of Fire's specific rule dealing 2x fire damage to undead. Protection from Energy will absorb the full amount remaining of 60 fire damage, and the Undead has 0 fire absorption left. Of the 40 remaining fire damage, Resist Energy will now reduce this damage by 20 fire damage, because Protection from Energy has now been fully exhausted. The Undead takes 20 fire damage.
Undead gets hit by Wall of Fire for 25 damage. This is increased by 100% to 50 damage for Wall of Fire's specific rule dealing 2x fire damage to undead. Resist Energy will now reduce this damage by 20 fire damage. The Undead takes 30 fire damage.
Okay, that's how it played out in my head. Thank you all for confirming.