Similar artist API (also works for movies and TV shows).
TasteDive API is a free Music API that requires apiKey authentication, is served over HTTPS and has unconfirmed CORS support.

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