so i want to build mobile app with flutter like moodleApp, so that app just fetch api from the existing moodle web, then, does moodle provid API to be used freely? or any other way?
Yes. Moodle provide API
https://docs.moodle.org/dev/Core_APIs
https://docs.moodle.org/dev/Web_service_API_functions
https://docs.moodle.org/dev/Creating_a_web_service_client
Example : https://example.com/moodle/webservice/rest/server.php?wstoken=...&wsfunction=...&moodlewsrestformat=json