If it's my focus, I play an action spell. It resolves, is it still my focus or does it automatically pass?

After your action spell resolves, your focus automatically passes to your opponent.

According to Rule 346 and the associated FAQ, once the last item on a non-initial chain resolves and the game returns to an Open State, focus automatically passes to the next player.

Here is the breakdown of why this happens:

1. Opening the Chain: You used your focus to play an [Action] spell, moving the game state from Open to Closed.
2. Resolution: Once the spell resolves and the chain is empty, the game state returns to Open.
3. Focus Shift: Per Rule 346, focus passes to your opponent. They now have the opportunity to either start a new chain with their own actions/reactions or pass focus back to you.

The "Initial Chain" Exception: The only time focus does not pass after a chain resolves is if it was the Initial Chain of the showdown (triggered by "When I Attack" or "When I Defend" abilities). In all other cases, such as the one you described, focus shifts automatically.

Can you play actions back-to-back? No. You cannot play multiple action spells consecutively. You can only play a second action spell if your opponent receives focus after your first spell resolves and they choose to pass focus back to you without playing anything themselves (FAQ 8470).