Can my opponent attack and play an action, and can I respond with an action?

No, you cannot respond to an Action spell with another Action spell.

When your opponent plays an Action spell, they start a Closed State (a chain). Once a chain is open and has items on it, you may only play cards or abilities with the [Reaction] keyword to respond.

According to Riftbound mechanics:

1. [Action] cards can only be played when the state is Open (no chain exists).
2. [Reaction] cards can be played in both Open and Closed states.

Sequence:

1. Your opponent plays an Action spell, starting a chain. The state is now Closed.
2. You cannot play an Action spell because the state is Closed. You may only play a [Reaction] card.
3. Once the chain fully resolves (including any Reactions that were added), the state becomes Open again.
4. Only then, when focus passes back to you, can you play an Action spell.

This is consistent with several RiftJudge FAQs, including FAQ #1787 and #2818, which clarify that players can only respond to Actions with Reactions, and must wait for the chain to resolve before they can play an Action themselves.