Casting a spell for its surge cost doesn't change its mana cost or its mana value.

The other spell that you or a teammate cast can be one that's resolved, one that was countered, or (for instants with surge) one that's still on the stack.

For some cards, surge represents only an alternative cost, a discount that applies if you or a teammate has cast another spell this turn. Other cards, like Reckless Bushwhacker, have additional abilities or effects if you paid the surge cost to cast the spell.

Grip of the Roil tracks the creature, but not its controller. If the creature changes controllers before its first controller's next untap step has come around, then it won't untap during its new controller's next untap step.

If an instant or sorcery spell cast for its surge cost is copied, the copy is also considered to have had its surge cost paid.

Grip of the Roil can target a creature that's already tapped. It still won't untap during its controller's next untap step.