As always, both apply before any modifiers to damage taken.
You're referring to "increased/reduced damage taken", not for example "25% of Elemental Damage taken as Chaos Damage" on Incandescent Heart, right? My understanding from how Armour's worked previously is that something like Incandescent Heart with this chest should convert 25% of the Elemental Damage before Armour is applied.
Yes. "Modifiers to damage taken" means modifiers to the damage taken value, after it has been calculated (via resists/armour). Modifiers to which type of damage you take happen before any mitigation because otherwise there would be no point.