Tide Shaper will get +1/+1 as long as an opponent controls any land with the Island land type, not just ones named Island.

A land that becomes an Island gains "{T}: Add {U}" and loses all other abilities. It loses any other land types, but it doesn't lose any types or supertypes, such as creature, legendary, or snow.

If Tide Shaper leaves the battlefield before its triggered ability resolves, the target land will not become an Island.

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

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 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.

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

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

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