If I start combat and play Counter Strike, then it resolves. The chain is empty. Is it still my priority? Can I play first still, or is it impossible after I start combat and start a chain?

No, it is not your priority, and you cannot start another chain immediately.

According to Rule 340.2.a and RiftJudge FAQ #1968, during a showdown, once the chain resolves and the turn returns to an Open State, focus automatically passes to your opponent.

Here is the breakdown of your situation:

1. Opening the Showdown: You initiate combat. You gain the "Attacker" designation and gain Focus.
2. Starting a Chain: You play Counter Strike (or another action) to start a chain. Because you started the chain, it is now a Closed State.
3. Chain Resolves: The chain resolves, and Counter Strike creates its replacement effect.
4. Priority and Focus: Once the chain is empty and the state returns to Open, Focus automatically passes to the defender (your opponent).

Can you play again? Yes, but you must wait. After your opponent gains Focus, they have the opportunity to either play an action (starting a new chain) or pass. If they pass, Focus returns to you, and you can then play another action if you wish. Both players must pass consecutively without starting a new chain for the showdown to proceed to the Combat Damage Step (as detailed in RiftJudge FAQ #3636 and FAQ #4166).

In short: You cannot act twice in a row. You must allow your opponent the opportunity to respond to the state of the board after your first chain resolves.