Annihilator abilities trigger and resolve during the declare attackers step. The defending player chooses and sacrifices the required number of permanents before they declare blockers. Any creatures sacrificed this way won't be able to block.
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.
Kozilek's first ability triggers as you cast it, and that ability resolves before the spell itself. It resolves even if the spell is countered.