You too!

Any double-faced card has only the properties of its front face while it's anywhere other than the battlefield (or in the case of Modal Dual Faced Cards like Blex, Vexing Pest  ^Flip, the stack).

The card will go back to being Westvale Abbey while it's in the graveyard, so it can't be targeted by Reanimate.

If an effect does reanimate a DFC, it'll only reanimate it on its front side unless that effect specifically says otherwise. Crucible of Worlds and Splendid Reclamation can each bring back out the Westvale Abbey, but it will only be a Westvale Abbey. You'll need to transform it again. Same principle with triggered reanimation effects like Marchesa, the Black Rose.

The card being treated as its front face is an immediate thing that doesn't use the stack. I.E., if Ormendahl dies, there is no moment before it flips back to Westvale Abbey in the graveyard where you are able to cast Back for More to bring it back first. Likewise if Ormendahl is targeted with a Cloudshift, it'll be exiled and immediately turned front-face up again, then reenter the battlefield as Westvale Abbey.

Deadline's up. Here's hoping he likes it.

Yes, it still works. Hashaton triggers on the game action of discarding, and doesn't care about checking to see where the card ended up.

Likewise, you can discard a madness card like Shadowgrange Archfiend and cast it and still create an eternalized copy of it.

You don't, no. Cairn Wanderer's ability gives it keyword abilities while it's a permanent on the battlefield. The card itself doesn't have those abilities while it's not on the battlefield, so Indominus Rex doesn't get them from discarding it.

Still might be a decent inclusion in the deck since the other keyword cards end up in your graveyard for the Cairn Wanderer.