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.

Eldrazi Conscription is an Eldrazi. However, it doesn’t turn the enchanted creature into an Eldrazi.