Most file actions are done through your cloud provider, such as moving, deleting and renaming files, but this will come soon! In the meantime, you'll need to open your cloud provider's website - such as Gdrive, OneDrive or Dropbox and manually delete, move or rename there.
You can copy files by opening the document you wish to copy, then clicking on Document > Make a copy. You'lll then be prompted to either open the copy in the same tab or a new tab. Click on Document > Save to then save.
If you rename a file, then it will still have the old name in Recent Files until you open the newly named file.
If you delete a file it will still appear in the Recent Files panel of the Document picker but you will not be able to open it - you'll receive a warning that the file couldn't be found in the cloud drive.