How does ambush work on an empty Battlefield? If opponent moves to one open Battlefield, can I ambush there?

No, you cannot use Ambush to play a unit to an empty battlefield.

According to Rule 822.1.b and RiftJudge FAQ #9556, the Ambush keyword has two specific requirements:

1. Presence Requirement: You must already control at least one unit at the target battlefield.
2. Timing Permission: It grants you the [Reaction] keyword, allowing you to play the unit even if the game state is Closed (such as during a showdown), provided the first requirement is met.

Regarding your scenario:

If your opponent moves a unit to an empty battlefield, that battlefield is currently unoccupied. Because you have no units there, you do not meet the requirement to use the Ambush keyword. Therefore, you cannot play a unit with Ambush to that location using the Ambush ability.

Key takeaways:

• Ambush is not a way to deploy to empty locations: It is designed to allow you to reinforce a battlefield where you already have a presence.
• Requirement Check: The condition (controlling a unit at the location) is checked at the moment you declare you are playing the card. If you do not have a unit there, the location is not valid for Ambush (Rule 822.3).
• No "Ambush from Base": Even if you have units in your base, they do not count as being "at the battlefield," so they do not satisfy the Ambush requirement for a battlefield (FAQ #9556).