Approach My Molten Realm

• WWizards of the Coast2010-06-15
  Official Ruling
  The effect doesn’t wear off until just before your next untap step (even if an effect will cause that untap step to be skipped).
• WWizards of the Coast2010-06-15
  Official Ruling
  This ability applies no matter who or what the damage would be dealt to: a creature, a player, or a planeswalker. It also doesn’t matter who controls the source.
• WWizards of the Coast2010-06-15
  Official Ruling
  If multiple effects modify how damage will be dealt, the player who would be dealt damage or the controller of the permanent that would be dealt damage chooses the order to apply the effects. For example, Mending Hands says, “Prevent the next 4 damage that would be dealt to any target this turn” and Lava Axe says “Lava Axe deals 5 damage to target player or planeswalker.” Suppose a Lava Axe would deal 5 damage to a player who has cast Mending Hands targeting themselves. The player who would be dealt damage can either (a) prevent 4 damage first and then let this scheme’s effect double the remaining 1 damage, taking 2 damage, or (b) double the damage to 10 and then prevent 4 damage, taking 6 damage.
• WWizards of the Coast2010-06-15
  Official Ruling
  If a spell or ability divides damage among multiple recipients (such as Fireball does), the damage is divided before this effect doubles it.

Rulings via Scryfall