How can I find which users of my domain are using Google cloud services and API's? As far as I understand everyone on my (edu) domain is allowed to use these services but this could result in costs or unwanted data breaches.
As an administrator, I don't think you can view your users' use of Google Developers Console. However, you can disable access to all users (or all users in a subset of Organizations) by going to the CPanel (https://admin.google.com) > Apps > Additional Google Services > Google Developers Console (or clicking here).
Regardless, your organization will not be billed for your users' usage - if they meet the free quota, they won't be able to make additional calls until they provide payment information. Additionally, a Google Apps administrator must grant each application access to your domain's data (see here) - even applications created by domain users via the Google Developers Console.
So you can't track their use, but you can disable it. Even if you leave it enabled, it won't cost your organization anything and users won't be able to access sensitive data without an administrator's action.