ApiMedic offers a medical symptom checker API primarily for patients.
ApiMedic API is a free Sports & Fitness API that requires apiKey authentication, is served over HTTPS and has unconfirmed CORS support.

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Yes. The ApiMedic API is listed in the Sports & Fitness 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 ApiMedic API uses apiKey authentication, so you need to register for credentials before making requests.
CORS support for the ApiMedic API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The ApiMedic API is served over HTTPS, so it's safe to use in production.