Explain in greater detail how does Ivern work. Can I return BF to original if I conquer other BF?

To explain how Ivern works, it is important to distinguish between the different cards that share his name. Based on your question, you are referring to the ability to create Brush battlefield tokens, which is associated with the card Ivern, Green Father (as noted in the Unleashed patch notes).

How Ivern (Green Father) Works

When you play Ivern, Green Father, his ability allows you to replace an existing battlefield with a Brush battlefield token.

According to Rule 184.8, a Brush battlefield token has the following text:

• "Bird, Cat, Dog, Poro, and Ivern units here have +1 [M]"
• "When you score here, you may replace this with the battlefield it replaced."

This means the Brush token acts as a battlefield that provides a passive Might bonus to specific unit types. It remains in play until you choose to replace it or another game effect removes it.

Can you return the battlefield to its original state if you conquer another battlefield?

No. You cannot return the Brush token to its original battlefield state by conquering a different battlefield.

The ability on the Brush token specifically states: "When you score here, you may replace this with the battlefield it replaced."

• "Here" refers to the specific battlefield location where the Brush token is currently located.
• The ability is triggered by the act of scoring at that specific location.
• Conquering or scoring at a different battlefield does not satisfy the condition to trigger the replacement ability on the Brush token.

In summary, the Brush token only reverts to the original battlefield when you score at the location where the Brush token is currently present.