The control used for listing files and folders inside the Editor's Document Manager is RadFileExplorer and in order to display some date-related information about each file you can create a custom column in it. This can be done by going through the following steps:
You might find useful information on how to add code-behind to the Editor's dialogs in this KB article: Displaying single upload control in the FileBrowser Upload manager
I hope this information will be helpful for you.
Check out the Telerik Platform - the only platform that combines a rich set of UI tools with powerful cloud services to develop web, hybrid and native mobile apps.