1- There is an API from Crowdin https://support.crowdin.com/api/api-integration-setup/
2- Do you have an official reply from Crowdin on no API support?
3-Just for curiosity, why do you need API for Crowdin?
It would be useful to see an official post from Utopian on this issue, stating the requirements (and workflow) so the problems you have found could get a solution in the future (for Crowdin and for any other translation platform)
Hey! Utopian only has an API for project owners, not for the users. That being said, a lot has changed in the last 4 days, you can read the update post here. The discussion of bringing Crowdin back to Utopian is still going.