Feel free to ask questions here about how certain cards interact and some tips on how the brawl works. Below is what I gathered so far:
All cards that discard: Once discarded, they are out of your deck for good. Cards that discard: Deathwing, Tracking, Felstalker (Succubus), etc.
Cards Returned to hand: Whenever a card is returned to your hand, a second copy will be permanently added to your deck. Cards that return to hand: Sap, Freezing Trap, Youthful Brewmaster, Shadowstep, etc.
Cards Put in Play Other Than Normal Play: This works very similar to the discard function; once pulled from your hand or deck, it's gone. Cards with that effect: Captain Hooktusk, Piloted Reaper, Duel!, Masked Contender, Flark's Boom-Zooka, Coffin Crasher, etc.
Tokens: Tokens work the same way as cards being returned to hand; once added to your hand, they are permanently added to your deck.
Cast When Drawn: Unless actually drawn from an effect that draws cards, these do not trigger. They just float in your deck and hand. Cards that add cards to your deck: Wrenchcaliber, Hakkar, The Soulflayer, etc.
...'s Scheme: Doesn't actually upgrade since it shuffles back into your deck.
Lackeys and other card generators: Works the same as when a minion is returned to your hand; the card is permanently added to your deck.
Handbuffs and Cost Reduction Cards: Unless the card was played the same turn the effect occurred, the effect does not remain. Cards with these effects: Prismatic Lens, Ferraki Battleaxe, Far Sight, Luna's Pocket Galaxy, Glowstone Technichian, Call to Adventure, Predatory Instincts, Wing Blast, Soul Infusion, Jepetto Joybuzz, etc. Cards that add cards to your hand will still be added, but won't be modified like they were unless played in the same turn. Cards with these effects: Splintergraft, Academic Espionage, Dire Frenzy, Spirit of the Dead, Bog Slosher, etc.
Echo effects, Twinspells, and cards that repeat themselves: A copy is added to your deck each time you play it plus the one in hand. Formula: X echo cards played, X shuffled in your deck and 1 in hand which shuffles in at the end of the turn. 3 echo cards played, 4 cards shuffled back into the deck total. For Twinspells, a twinspell copy will be shuffled, and a non-twinspell copy will also be shuffled.
Unseen Saboteur: This will permanently remove the played spell from your opponent's deck.
Dr. Morrigan: The minion swapped from your deck is gone from your deck permanently. A second copy of Dr. Morrigan will stay in your deck. This will repeat every time the deathrattle is triggered.
The Soularium: This doesn't actually discard the cards. For this brawl, it works as just a Draw 3 cards.
Demonic Project and Prince Liam: The minion transformed is permanently changed and will remain in your deck.
Archivist Elysiana: Other than the cards in your hand, this removes ALL cards in your deck including the Archivist Elysiana shuffled in after she was played.
Dreampetal Florist: Her affect happens at the end of your turn, so the cost reduction will occur after you draw a fresh hand.
Shirvallah and Grave Horror: Card works just like constructed.
Please leave any questions, comments, or even how to play suggestions on the below thread. As a courtesy, I ask that this be for people who want to learn how this brawl works. Please leave any salty comments in the salt thread. I personally enjoy this brawl, but I don't like the fact that all these interactions are kind of a trial-and-error system.