@Bastian I think this link will help you answer your questions. It is also GDPR compliant.
Azure Cognitive Services Translator is a cloud-based machine translation service and is part of the Azure Cognitive Services family of cognitive APIs for building intelligent apps. Customer data submitted for translation to Azure Cognitive Services Translator (both standard and custom models), Speech service, the Microsoft Translator Speech API, and the text translation features in Microsoft Office products are not written to persistent storage. There will be no record of the submitted text or voice, or any portion thereof, in any Microsoft data center. The audio and text will not be used for training purposes either.
The documents you upload using Custom Translator (portal or APIs) are stored encrypted in your workspace. If you signed up for a Translator subscription with customer-managed keys, you may use it by associating your Translator subscription with a new workspace in Custom Translator. Custom Translator uses your uploaded documents exclusively to provide your personalized translation system and does not use it for any other purpose. The documents you upload to Custom Translator will be stored in the Azure region you selected when you created your Translator key until you delete them or until your account expires