Battlefield Thaumaturge

• WWizards of the Coast2014-04-26
  Official Ruling
  The cost reduction is per target creature, even if the spell targets a creature more than once.
• WWizards of the Coast2014-04-26
  Official Ruling
  Heroic abilities won't trigger when a copy of a spell is created on the stack or when a spell's targets are changed to include a creature with a heroic ability.
• WWizards of the Coast2014-04-26
  Official Ruling
  To calculate the total cost of an instant or sorcery spell you're casting, start with the mana cost (or alternative cost, if applicable), add all cost increases (including additional costs such as those imposed by strive abilities), then subtract all cost reductions (such as the one created by Battlefield Thaumaturge's first ability).
• WWizards of the Coast2014-04-26
  Official Ruling
  Heroic abilities will resolve before the spell that caused them to trigger.
• WWizards of the Coast2014-04-26
  Official Ruling
  The cost reduction created by Battlefield Thaumaturge's first ability can reduce only the generic portion of the spell's total cost. Colored mana requirements aren't affected.
• WWizards of the Coast2014-04-26
  Official Ruling
  Battlefield Thaumaturge's first ability doesn't change that spell's mana cost or mana value. It changes only the amount you actually pay (the “total cost” of the spell).
• WWizards of the Coast2014-04-26
  Official Ruling
  Heroic abilities will trigger only once per spell, even if that spell targets the creature with the heroic ability multiple times.

Rulings via Scryfall