Is there a REST API available in MoodleCloud to exchange data with WordPress (or any other common systems).
Yes, there is an extensive REST API in Moodle. The main documentation is in https://docs.moodle.org/38/en/Web_services. You'll find a lot of information in your Moodle site itself, in the web services section of the site administration. A good starting point is /admin/settings.php?section=webservicesoverview on your site.