Absorb Essence effectively becomes "Gain 3 Energy. Target Spirit gains Any Element and 1 Energy." (You cannot follow the instruction "Move 1 of target Spirit's Presence to your 'Deep Slumber' track", because you do not have a Deep Slumber track.)
Ocean's Special Rules define what "Drown" means: "Destroy Drowned pieces, placing Drowned Invaders here [on Ocean's playmat]." So if another Spirit Drowns an Invader, it is Destroyed (by that Spirit), then goes onto Ocean's playmat. Similarly, since Terror Stalks the Land defines what "Abduct" means, abducted pieces go to The Endless Dark whether or not Breath of Darkness Down Your Spine is the one using the Power.