Drag & Drop out of a File Attachment field

Dragging and dropping a single file isn't possible to my knowledge, you have to consider that the file attachment you see is just a link to the underlying file so you have to bring it forth and actually download or programatically get the contents for you machine/browser to be able to drag and drop it. 

Being able to download them all you could do with a code page and loop through all the file attachments to get the latest version and download, your browser will likely prompt you to allow it to download multiple things at once as a security measure.