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The lands that will be destroyed aren’t chosen until Burning of Xinye resolves.
Burning of Xinye targets only an opponent. If that player is an illegal target by the time Burning of Xinye resolves, the entire spell doesn’t resolve.
In a multiplayer game, only lands controlled by two players (you and the targeted opponent) are destroyed. However, Burning of Xinye will deal 4 damage to each creature, even those controlled by other players.
A land with a regeneration shield on it will regenerate from Burning of Xinye’s destruction effect. However, the spell or ability that creates that shield must be cast or activated before Burning of Xinye starts to resolve.
As Burning of Xinye resolves, first you destroy four lands you control (all at the same time), then the targeted opponent destroys four lands they control (all at the same time). That player chooses which of their lands to destroy. Neither of you can choose to destroy a land with indestructible.
