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

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as an evoke cost), add any cost increases, then apply any cost reductions. The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.

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.

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.