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OK, it's pretty clear the way Resist Energy and Protection from Energy interact. The protection absorbs full damage (unresisted) until the shield drops then the resistance kicks in. Protection from energy overlaps (and does not stack with) resist energy. If a character is warded by protection from energy and resist energy, the protection spell absorbs damage until its power is exhausted.
But how do they interact with Fire Shield? namely this line, You take only half damage from cold-based attacks. If such an attack allows a Reflex save for half damage, you take no damage on a successful saving throw.
Does the Shield's take half damage come in before the Resist or Protection?
Does the Protection kick in first absorbing full damage until it drops?
Does the half damage go first then the Resistance subtracts what is left?
I only found one relevant post pertaining to the question and there was only one reply. Inquiring minds want to know.
The typical trend of the general rules is not not allow for double dipping or stacking of this sort. The safe bet is to go with whatever situation is worse off. Meaning, the protection takes full damage and doesn't take into account the resist amount or the half damage from the shield. Once the protection is gone, my guess is you would apply the resist to any further damage done and then halve it after. Otherwise you would be getting twice the amount of resist (half damage first then the resist amount applied) which goes against the grain of the normal rules.