If I move to a battlefield with a unit and it's open, and he plays Void Seeker, an action card, can he? Is it a noncombat showdown? Or only reactions?

When you move a unit to an empty battlefield, you create a non-combat showdown. Because the battlefield was empty, it becomes contested, which triggers a showdown (Rule 429.1).

Regarding your questions about playing Void Seeker:

1. Can they play Void Seeker?

Yes. Void Seeker is an [Action] spell, and [Action] spells can be played during a showdown when the state is open.

2. Is it a non-combat showdown?

Yes. Moving to an empty battlefield creates a showdown, but it is not a combat showdown (FAQ #5551). Combat showdowns only occur when moving to a battlefield already occupied by an enemy unit (Rule 4401).

3. Are only reactions allowed?

Whether you can play an [Action] spell depends on the current State of the turn:

• Showdown Open State: If no chain exists (the chain is empty), the turn is in a Showdown Open state (Rule 310.3). In this state, the player with focus can start a new chain by playing an [Action] or [Reaction] spell.
• Showdown Closed State: Once a player plays a spell, a chain is created, and the turn enters a Showdown Closed state (Rule 310.4). In a closed state, only cards or abilities with the [Reaction] keyword can be played or activated (Rule 309.1.a).

Summary of the flow:

1. Showdown Begins: The turn is in a Showdown Open state.
2. Playing the Action: If the opponent has focus, they can play Void Seeker (an [Action] spell) to start a chain.
3. State Change: As soon as Void Seeker is played, the chain exists, and the turn becomes Showdown Closed.
4. Adding to the Chain: While the chain is closed, you (or the opponent) can only add [Reaction] spells to the chain. You cannot play another [Action] spell until the current chain resolves and the state returns to Showdown Open.