Global Biodiversity Information Facility.
GBIF API is a free Science & Math API that requires no API key, is served over HTTPS and supports CORS, so it can be called from the browser.

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Yes. The GBIF API is listed in the Science & Math 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 GBIF API requires no authentication, so you can start making requests without signing up.
Yes. The GBIF API supports CORS, so front-end JavaScript can call it directly.
Yes. The GBIF API is served over HTTPS, so it's safe to use in production.