MailRambo
Verify email deliverability with a strict yes/no, disposable and catch-all detection

Check a domain's SPF, DKIM, DMARC and MX records and get what to fix, with the values to publish.
MailSenpai DNS Check API is a free Email API that requires no API key, is served over HTTPS and supports CORS, so it can be called from the browser.
Free JSON API that checks a domain's SPF, DKIM, DMARC and MX records and returns what to fix, with the values to publish. No key, CORS enabled.
Details from en.mailsenpai.com.

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The MailSenpai DNS Check API is provided by MailSenpai (en.mailsenpai.com). Free JSON API that checks a domain's SPF, DKIM, DMARC and MX records and returns what to fix, with the values to publish. No key, CORS enabled.
Yes. The MailSenpai DNS Check API is listed in the Email 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 MailSenpai DNS Check API requires no authentication, so you can start making requests without signing up.
Yes. The MailSenpai DNS Check API supports CORS, so front-end JavaScript can call it directly.
Yes. The MailSenpai DNS Check API is served over HTTPS, so it's safe to use in production.