If you want to copy a file in a top level site library to a sub site library, you can use "copy" in content and structure. Check the document in the source library, select "copy" from the actions drop down and select the destination library in the dialog box.
I've come across the folder problem you mention in a library web part added to a sub site too - I opened a ticket but support was unable to remedy it. It's possible to duplicate a library but it's a bit convoluted:
http://techtrainingnotes.blogspot.com/2009/03/sharepoint-one-library-multiple-sites.html