Do customers pay when they message my restaurant on WhatsApp?

No. Meta states that messages sent from a WhatsApp user to a business are not charged. Customers only use their normal mobile data to message you.

• This is Meta's rule for the WhatsApp Business Platform, written on its pricing page.
• Charges are on the business side, for messages the business sends, based on the message type.
• Check the current price list before you plan a campaign, because rates can change.