Does the Zealot Barbarian’s Divine Fury apply multiple times if you focus the same target?

The Path of the Zealot barbarian (Xanathar’s Guide to Everything, p. 11) gets the Divine Fury feature at level 3, which states:

At 3rd level, while you’re raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.

The RAI intent seems as though it should be the first successful hit to a creature on your turn deals an additional 1d6 damage, but it doesn’t seem as explicit as Sneak Attack, which states that it only happens once per turn.

Does Divine Fury truly work the same way as the rogue’s Sneak Attack, or can you proc Divine Fury multiple times if you focus fire?

Can a Zealot Barbarian apply Radiant rage damage?

Rage says

When you make a melee weapon attack using Strength, you gain a bonus to the damage roll that increases as you gain levels as a barbarian, as shown in the Rage Damage column of the Barbarian table.

And a Zealot Barbarian can

At 3rd level, while you’re raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.

Can the rage damage be radiant/necrotic, or does it have to be part of the weapon’s damage die? Is Divine Fury part of the weapon damage die?

Would a zealot barbarian’s divine fury trigger during an opportunity attack?

The Path of the Zealot barbarian (Xanathar’s Guide to Everything, p. 11) gets the Divine Fury feature at level 3, which states:

At 3rd level, while you’re raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.

Does it work like the Rogue’s Sneak attack, in that it can trigger on opportunity attacks, since it’s a different turn? Or does the "on each of your turns" bit make it not work.

What does the Death Ward spell do when a Zealot Barbarian’s Rage Beyond Death feature ends while they have three failed Death Saving Throws?

The death ward spell states:

[…] If the spell is still in effect when the target is subjected to an effect that would kill it instantaneously without dealing damage, that effect is instead negated against the target, and the spell ends.

One example of such an effect would be failing a third death saving throw. Ordinarily you would die immediately after failing your third death saving throw but this is not the case for the Zealot Barbarian currently Raging Beyond Death:

You still must make death saving throws, and you suffer the normal effects of taking damage while at 0 hit points. However, if you would die due to failing death saving throws, you don’t die until your rage ends, and you die then only if you still have 0 hit points

So what happens if the Barbarian has three failed death saves and then their Rage ends?
What instantaneously killing effect is the Barbarian being subjected to?
What exactly is negated by death ward?
Is the third death saving throw removed?

What happens when you cast Death Ward on a raging level 14 Zealot Barbarian who is at 0 HP?

Let’s say a Zealot Barbarian is using Rage Beyond Death and thus they do not fall unconscious at 0 HP. Let’s further say that they’re currently at 0 HP.

If death ward is cast on them, then by RAW it seems like they do not go back up to 1 HP. But what if they receive damage afterwards? Does death ward kick in and return them to 1 HP, or does it not kick in because you can’t drop to 0 HP while already at 0 HP?

How do I kill a 20th level raging Zealot Barbarian?

At 20th level, the Path of the Zealot barbarian (Xanathar’s Guide to Everything, p. 11) can rage indefinitely by virtue of starting a new rage just prior to their initial rage ending. This is confirmed by this question.

At 14th level, they also picked up the Rage Beyond Death feature, which lets them stay active at 0 hit points and regardless of how many death saves they’ve failed:

While you’re raging, having 0 hit points doesn’t knock you unconscious. You still must make death saving throws, and you suffer the normal effects of taking damage while at 0 hit points. However, if you would die due to failing death saving throws, you don’t die until your rage ends, and you die then only if you still have 0 hit points.

At 15th level, barbarians gain the Persistent Rage feature, meaning their rage ends only if they fall unconscious or choose to end it.

Given that the Barbarian can constantly remain in a state of rage, how can I ever reliably kill them? Reliably meaning they won’t get a save to negate the effect since they would be able to constantly cycle their Fanatical Focus to ensure rerolls on saves.