Cryptocurrencies Exchange.
Kraken API is a free Cryptocurrency API that requires apiKey authentication, is served over HTTPS and has unconfirmed CORS support.

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