Weather.
ColorfulClouds API is a free Weather API that requires apiKey authentication, is served over HTTPS and supports CORS, so it can be called from the browser.

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Yes. The ColorfulClouds API is listed in the Weather 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 ColorfulClouds API uses apiKey authentication, so you need to register for credentials before making requests.
Yes. The ColorfulClouds API supports CORS, so front-end JavaScript can call it directly.
Yes. The ColorfulClouds API is served over HTTPS, so it's safe to use in production.