Companion cards are played with the errata - they can be put in your hand for (3) as a sorcery from outside the game. They must be revealed at the start of each game if they're being used in a deck.
There is one Un-set card: Booster Tutor. Each draft we'll make a single extra pack while creating the draft packs, just in case some drafts this card. That one pack is what the card will 'tutor for' in all games that draft (so they will all be cards that were not seen that draft).
One card 'cares' if you have snow-covered lands - Tainted Pact, since it technically gives you more unique cards, but not because of snow mana/snow permanents, etc.
No cards are included with multiplayer-focused keywords like Monarch. There's no Day/Night, Poison, Energy, Initiative. There are a few Vehicles, and a single Battle.