RTD.
Transport for Denver, US API is a free Transportation API that requires no API key, is only available over HTTP and has unconfirmed CORS support.

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Deutsche Bahn (DB) API
Yes. The Transport for Denver, US API is listed in the Transportation 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 Transport for Denver, US API requires no authentication, so you can start making requests without signing up.
CORS support for the Transport for Denver, US API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
No. The Transport for Denver, US API is only available over plain HTTP, which browsers block on HTTPS sites. Call it from a server instead.