Breaker of Creation's triggered ability will resolve before Breaker of Creation does. If Breaker of Creation is countered or otherwise leaves the stack in response to that triggered ability, the triggered ability will still resolve as normal.

If a creature with annihilator is attacking a planeswalker, and the defending player chooses to sacrifice that planeswalker, the attacking creature continues to attack. It may be blocked. If it isn't blocked, it simply won't deal combat damage to anything.

Annihilator abilities trigger and resolve during the declare attackers step. The defending player sacrifices the required number of permanents of their choice before they declare blockers. Any creatures sacrificed this way won't be able to block.