The chat should also work without websockets if needed, although I really suggest ensuring websockets work. However, without your configuration of your webserver we can’t help you further with that.
As for chat: Ensure that you have “Chat” enabled within the backend and at least one agent being online with chat functionality enabled in the frontend. Also, your agent needs to have the same topics enabled you’re testing on.
As Zammad has no chatbot functionality, we will not display the “chat with us button” if no one is available to chat with. This is to reduce frustrations on your customers end.