National Plan & Provider Enumeration System, info on healthcare providers registered in US.
NPPES API is a free Health API that requires no API key, is served over HTTPS and has unconfirmed CORS support.

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Yes. The NPPES 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.
No. The NPPES API requires no authentication, so you can start making requests without signing up.
CORS support for the NPPES API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The NPPES API is served over HTTPS, so it's safe to use in production.