Preacher of the Schism

• WOTC Official Reminder Textofficial rules
  Deathtouch — Any amount of damage this deals to a creature is enough to destroy it.

• WWizards of the Coast2023-11-10
  Official Ruling
  Preacher of the Schism's middle ability triggers only if it attacks a player. It won't trigger if Preacher of the Schism attacks a planeswalker or battle, no matter what its controller's life total is.
• WWizards of the Coast2023-11-10
  Official Ruling
  If you are tied for most life and Preacher of the Schism attacks another player who is tied for most life, both its middle and its last ability will trigger.
• WWizards of the Coast2023-11-10
  Official Ruling
  Once Preacher of the Schism's middle ability triggers, it doesn't matter what happens to players' life totals before the ability resolves. You'll create a Vampire token even if the player Preacher of the Schism attacked doesn't have the most life as the ability resolves.
• WWizards of the Coast2023-11-10
  Official Ruling
  Similarly, once Preacher of the Schism's last ability triggers, it doesn't matter what happens to players' life totals before the ability resolves. You'll draw a card and lose 1 life even if you don't have the most life as the ability resolves.

Rulings via Scryfall