Supermarket Data.
Kroger API is a free Food & Drink API that requires apiKey authentication, is served over HTTPS and has unconfirmed CORS support.

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Alcohol
Yes. The Kroger API is listed in the Food & Drink category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The Kroger API uses apiKey authentication, so you need to register for credentials before making requests.
CORS support for the Kroger API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The Kroger API is served over HTTPS, so it's safe to use in production.