Access to the data from the CMS - medicare.gov.
CMS.gov API is a free Health API that requires apiKey authentication, is served over HTTPS and has unconfirmed CORS support.

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