1. Is the best way to delete unneeded qvw files to just delete theem from your root/published location?
Yes, its good practice, but prior to that make sure you delete tasks first ( if any available on that document).
2. My Document Administrator has full control of the root and mount folders, but when she publishes a document it only gives her read access to the document. She can't delete her original test document.
Yes, make sure that your user belong to QlikView administrator and local administrator too.
Let me know if that worked