A spell or ability that counters spells can still target Urza's Rage. When that spell or ability resolves, Urza's Rage won't be countered, but any additional effects of that spell or ability will still happen.

If the target for Urza's Rage becomes an illegal target, the spell won't resolve and will be put into its owner's graveyard with no effect. This is true even if its damage can't be prevented and even though it can't be countered.

The kicker ability doesn't let you pay a kicker cost more than once.

If a card or token enters as a copy of a permanent, the new permanent isn't kicked, even if the original was.

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.

If a spell's kicker cost was paid, the spell is "kicked."

If you put a permanent with a kicker ability onto the battlefield without casting it, you can't kick it.

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.