How should I write my AI agent's prompt, and should I load the business website as knowledge?

Use the default format you get when you create an agent. It is the recommended structure: a personality (for example a warm, friendly agent), the tone, the goal, the guardrails, facts about the business, and FAQs. Because it is organized, if the AI says something wrong you can go to the matching FAQ and edit it, and if it did not know an answer you add that answer to the FAQs.

Put only what is specific to the business into the prompt as facts and FAQs: the business name, hours, address, pricing and common questions. The AI already has general knowledge, so a flooring company does not need an article about granite and a dentist does not need an explanation of crowns. Loading a client's whole website into a knowledge base is usually not needed, because most business websites are full of SEO articles the AI does not need.

There is no secret prompt. Tell the AI what you want, including any script the client wants it to say.