Recoup is a term used to describe modifiers that recover some of the damage taken from hits as energy shield, life, or mana over 4 seconds.
Yes. Each source of Recouping Life, Mana or Energy Shield is entirely independent.
Players innately Recoup 12% of Elemental Damage taken as Energy Shield per Absorption Charge, so gaining Absorption Charges will cause you to Recoup ES, and Graven’s Secret allows you to gain those charges. This modifier can be seen in the character panel if you have nonzero maximum Absorption charges, and in the reminder text of stats that allow you to gain those charges, and is explicitly described as Recouping. The other mentioned things are not Recouping – if they were, they would be described using that word.
Recovery of energy shield, life, and mana through recoup is scaled by increases and reductions to energy shield, life, and mana recovery rate, respectively.
Does damage taken recouped stack?
Yes. Each source of Recouping Life, Mana or Energy Shield is entirely independent.
Are these considered as recoup? (Graven's Secret, Doppelgänger Guise, Juggernaut's Unbreakable)
Players innately Recoup 12% of Elemental Damage taken as Energy Shield per Absorption Charge, so gaining Absorption Charges will cause you to Recoup ES, and Graven's Secret allows you to gain those charges. This modifier can be seen in the character panel if you have nonzero maximum Absorption charges, and in the reminder text of stats that allow you to gain those charges, and is explicitly described as Recouping. The other mentioned things are not Recouping - if they were, they would be described using that word.
For the belt Graven's Secret, does physical damage taken as fire/cold/lightning work with the Absorption Charge elemental damage recoup mechanic?
Yes.