Rushing River

• WOTC Official Reminder Textofficial rules
  Kicker — Kicker [cost] (You may pay an additional [cost] as you cast this spell.)

• WWizards of the Coast2004-10-04
  Official Ruling
  You choose a second target only if you choose to pay the Kicker cost.
• WWizards of the Coast2004-10-04
  Official Ruling
  You can sacrifice a tapped land.
• WWizards of the Coast2024-11-08
  Official Ruling
  To determine a spell's total cost, start with the mana cost (or an alternative cost if another card's effect allows you to pay one instead), add any cost increases (such as kicker), then apply any cost reductions. The spell's mana value remains unchanged, no matter what the total cost to cast it was.
• WWizards of the Coast2024-11-08
  Official Ruling
  If you put a permanent with a kicker ability onto the battlefield without casting it, you can't kick it.
• WWizards of the Coast2024-11-08
  Official Ruling
  The kicker ability doesn't let you pay a kicker cost more than once.
• WWizards of the Coast2024-11-08
  Official Ruling
  If a card or token enters as a copy of a permanent, the new permanent isn't kicked, even if the original was.
• WWizards of the Coast2024-11-08
  Official Ruling
  If you copy a kicked spell on the stack, the copy is also kicked. If the copied spell is a permanent spell, the token the copy of that spell becomes when it enters is also kicked.
• WWizards of the Coast2024-11-08
  Official Ruling
  If a spell's kicker cost was paid, the spell is "kicked."

Rulings via Scryfall