To export data from Mailfence, you can follow these steps:
1. Settings

2. Account -> Back-up:

3. Click on Export after choosing an element that you want

Note: The restriction on backup file size does applies for performance reasons e.g., for documents: up to 250 MB of data, for e-mails: up to 250 MB of data. If you would like to backup large volume of data, please use respective external clients e.g., CardDAV/EAS client for contacts, CalDAV/EAS client for calendar events, WebDAV client for documents, and IMAP client for emails.
For exporting a specific email: Right-click on the message in the message list panel -> Archive -> Download.

For exporting a specific document: Right-click on the document -> Download.

For exporting a specific calendar event: Right-click on the calendar event -> Export.

For exporting a specific contact: Right-click on the contact -> Export (vCard).

For exporting your OpenPGP keypair(s)/other public keys, please check this article.