Illusion // Reality

• WWizards of the Coast2022-12-08
  Official Ruling
  Each split card has two names. If an effect instructs you to choose a card name, you may choose one of those names, but not both.
• WWizards of the Coast2022-12-08
  Official Ruling
  To cast a split card, choose one of its halves to cast. There's no way to cast both halves of this split card.
• WWizards of the Coast2022-12-08
  Official Ruling
  A split card's characteristics are a combination of its two halves while it is not on the stack. For example, Assault // Battery has a mana value of 5 while it is in your library. If an effect allows you to search your library for a card with mana value 4 or less, you can't find Assault // Battery.
• WWizards of the Coast2022-12-08
  Official Ruling
  Split cards have two card faces on a single card. The characteristics of the half you didn't cast are ignored while the spell is on the stack.
• WWizards of the Coast2022-12-08
  Official Ruling
  If an effect allows you to cast a spell with certain characteristics, consider only the characteristics of the half you're casting. For example, if an effect allows you to cast a sorcery spell with mana value 2 or less from among cards in your graveyard, you could cast Assault this way, but not Battery.
• WWizards of the Coast2022-12-08
  Official Ruling
  If you copy a spell that's half of a split card, the copy copies that same half. For example, if you copy Assault, the copy is also Assault, not Battery.
• WWizards of the Coast2022-12-08
  Official Ruling
  Each split card is a single card. For example, if you discard a split card, you've discarded one card, not two. If an effect counts the number of sorcery cards in your graveyard, Assault // Battery counts once, not twice.

Rulings via Scryfall