QIf I have this follower on my field with 20 Armageddon counters, and an opponent has a Lyrial, Archer Throne on their field, will their leader take 10 damage from this follower's Strike ability?

AYes. Since effects are applied in written order, this follower's Strike ability will destroy the enemy Lyrial, Archer Throne before dealing damage to each enemy leader. Therefore, Lyrial, Archer Throne's ability will not take effect.

QThis follower is on my field with 30 Armageddon counters, Opponent A has an Ancient Protector on their field, and their leader has 10 defense or less. What happens when I attack with this follower?

AFirst, you apply the effects of the Strike ability in written order, so you destroy each enemy follower on the field and then deal 10 damage to each enemy leader. At this point, Opponent A's leader's defense has become 0 or less, so their Ancient Protector's ability triggers and becomes pending until the Strike ability is fully resolved.

Then, you resolve the rest of the Strike ability, causing each opponent to lose the game, excluding Opponent A because they still have Ancient Protector on their field.

Finally, Ancient Protector's ability is resolved, setting Opponent A's leader's defense to 1.

QI'm playing against 3 other players. I have this follower on my field with 30 Armageddon counters, and one of my opponents has an Ancient Protector on their field. What happens to the other 2 opponents when I attack with this follower?

AAncient Protector prevents its controller from losing, so the two opponents without it on their field lose the game as a result of this follower's Strike ability.