Sword of Once and Future

• WOTC Official Reminder Textofficial rules
  Surveil — Look at the top N cards of your library. Put any number of them into your graveyard and the rest on top of your library in any order.
• WOTC Official Reminder Textofficial rules
  Equip — Equip [cost] ([cost]: Attach to target creature you control. Equip only as a sorcery.)

• WWizards of the Coast2023-04-14
  Official Ruling
  If the card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
• WWizards of the Coast2023-04-14
  Official Ruling
  The card you cast may be one you just put into the graveyard with surveil or one already in the graveyard.
• WWizards of the Coast2023-04-14
  Official Ruling
  You choose whether or not to cast the instant or sorcery card as the triggered ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.
• WWizards of the Coast2023-04-14
  Official Ruling
  If you cast a card "without paying its mana cost," you can't pay any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, those must be paid to cast the card.
• WWizards of the Coast2024-01-12
  Official Ruling
  When you surveil, you may put all the cards you look at back on top of your library, you may put all of those cards into your graveyard, or you may put some of those cards on top and the rest of them into your graveyard.

Rulings via Scryfall