Eye of Duskmantle

• WOTC Official Reminder Textofficial rules
  Lifelink — Damage dealt by this creature also causes you to gain that much life.

• WWizards of the Coast2024-02-02
  Official Ruling
  You may only cast spells this way by paying the appropriate amount of life. You may not pay their normal costs and may not pay any other alternative costs. You may still pay for additional costs, such as kicker costs. If the spell has mandatory additional costs, you must pay those.
• WWizards of the Coast2024-02-02
  Official Ruling
  If you cast a spell with in its mana cost this way, the only legal choice for X is 0.
• WWizards of the Coast2024-02-02
  Official Ruling
  “Cards in your graveyard you’ve surveilled this turn” includes cards you put into your graveyard while surveilling. It does not include cards you saw while surveilling, left on top of your library, and then put into your graveyard later that turn by other means.

Rulings via Scryfall