When Does Annihilator Trigger?

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.

Does annihilator trigger before combat?

Yes. Annihilator is a triggered ability, that triggers when the player declares the creature as an attacker. Removing the source does not remove the ability from the stack.

Does Annihilator target a player?

No, it doesn't target. You are not immune.