So if my Yone took damage and is from a 5 to a 4, and I move it to an empty battlefield, after gaining a point for Conquer, do I also heal, and then use his ability? Or because there was no defender, there was no combat, does he stay at 4?

To address your question regarding Yone, damage, and combat:

1. Does Yone heal?

No, Yone does not heal. As clarified in RiftJudge FAQ #9649, there is a critical distinction between a combat showdown and an open showdown:

• Combat Showdown: Occurs when a unit moves to an opponent-controlled battlefield. This triggers combat, which includes a "Combat Cleanup" step where all units heal.
• Open Showdown: Occurs when a unit moves to an empty (uncontrolled) battlefield. This is a showdown, but it is not combat. Because it is not combat, there is no combat cleanup, and therefore no healing occurs.

Moving to an empty battlefield allows you to conquer it and score, but it does not trigger the healing effects associated with the combat cleanup step.

2. How much damage does Yone's ability deal?

Yone deals damage equal to his full Might value, regardless of the damage marked on him. As established in RiftJudge FAQ #6749, #5165, and #1193, damage marked on a unit does not reduce its Might. Might and damage are separate concepts:

• A unit’s Might remains constant regardless of damage marked on it.
• If your Yone has a base Might of 5, he remains a 5 Might unit even if he has damage marked on him.
• When his ability resolves, he uses his current Might value to determine the damage dealt, not a reduced value.

Summary of the Sequence

1. Move Yone: You move Yone to an empty battlefield.
2. Conquer: You gain control of the battlefield and score a point.
3. Trigger Yone: Yone's ability triggers (as noted in FAQ #8405, he triggers at the end of a noncombat showdown in which he conquers).
4. Resolve Ability: Yone's ability goes on the chain. Upon resolution, it checks his current Might, which is not reduced by damage markers.
5. Status: Yone remains on the board with the damage markers still on him, as no combat cleanup occurred to heal him.

Note: I could not fully verify the specific mechanical claim that Yone's ability deals damage equal to his Might against the retrieved rules.