How does last carress interact with Elnuk Herd

Yes — Last Caress lets you play Elnuk Herd from face down to any battlefield, but its +3 [M] play effect must then target a friendly unit at the battlefield you actually played it to, and Elnuk still recycles itself because it was played from face down.

Last Caress overrides the normal "a hidden permanent must be played to the battlefield it was hidden at" restriction (811.1.d.1), so you can drop Elnuk on a different battlefield. The targeting restriction is a separate rule and does not go away: for a permanent played from face down, the play effect's targets must come from options at the battlefield it was played to (811.1.d.3 — that rule's own example is literally a "next unit you play can be played to any battlefield" spell). So if you move Elnuk elsewhere, the +3 [M] is locked to that new battlefield, not where it was hidden. Elnuk itself counts, so you'll always have at least one legal target.

Then "recycle me if I was played from face down" still fires — Elnuk goes to the bottom of your Main Deck after handing out the +3 [M]. The Buff counter Last Caress gave it is wiped when it leaves play (705), so that part is effectively wasted on the Elnuk; the real value is the +3 [M] on another friendly unit and the surprise placement.