Idol of False Gods's second ability will trigger whenever another Eldrazi you control is put into a graveyard from the battlefield, even if that Eldrazi isn't a creature.

If Idol of False Gods loses its abilities, the type-changing effect of its last ability will continue to apply to it. This is because effects that change an object's types are always applied before effects that remove abilities. In that case, if it has eight or more +1/+1 counters on it, it will be an Eldrazi kindred artifact creature. This is true even if it somehow gained its eighth +1/+1 counter after losing its abilities. If Idol of False Gods loses its abilities before gaining its eighth +1/+1 counter, it will have annihilator 2; otherwise, it won't.

In the rare case where enough -1/-1 counters are placed on Idol of False Gods to reduce its toughness to 0 or less while it's a creature because of the effect of its last ability, Idol of False Gods will be put into its owner's graveyard when state-based actions are performed. Effects that care about the number and types of counters that were on Idol of False Gods when it died will see both the +1/+1 and -1/-1 counters, and any effects that trigger "whenever a modified creature dies" will still trigger.

Kindred is a card type that allows noncreature cards to have creature types. For example, Echoes of Eternity is an Eldrazi (although not a creature) while on the battlefield and an Eldrazi card (although not a creature card) in zones other than the battlefield.

While it appears only on cards that already have other card types, kindred is a card type and will be counted by effects that refer to the number of card types among cards in a zone.

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.