Can you really create WordPress customers that may only view their very own uploads and not every one of the uploads in media library? If that's the case, how?

Ultimately, I wish to possess a password protected interface where I'm able to exchange files with my clients. Due to privacy issues, I don't want clients to have the ability to view one anothers files, or use whatever details about one another. Any tips on how to make this a reality could be greatly appreciated.

There's a wordpress plugin which should have the ability to handle this:

http://wordpress.org/extend/plugins/user-and-document-monitoring/

However, you may be best switching to Joomla to make the most of DocMan:

http://extensions.joomla.org/extensions/directory-a-documentation/downloads/10958