Annihilator abilities trigger and resolve during the declare attackers step. The defending player chooses and sacrifices the required number of permanents before he or she declares 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.

In a Two-Headed Giant game, the controller of an attacking creature with annihilator chooses which of the defending players is affected by the ability. Only that player sacrifices permanents. The choice is made as the ability resolves; once a player is chosen, it’s too late for anyone to respond.

Lethal damage and effects that say “destroy” won’t cause a creature with indestructible to be put into the graveyard. However, a creature with indestructible can be put into the graveyard for a number of reasons. The most likely reasons are if it’s sacrificed, if it’s legendary and another legendary creature with the same name is controlled by the same player, or if its toughness is 0 or less.