A number of business areas I work with use a folder structure to organise their Sharepoint housed documents (not ideal I know, but we\'re stuck with it).
I would l
Have a look at the content by type web part - http://codeplex.com/eoffice - probably the most flexible viewing web part.
I don't know of any out-of-the-box way to achieve this. As you say, this is not how SharePoint lists are intended used. It might work to create a custom site column displaying the path to the document, as this might be used in a filter. Have never tried it, though.
Use a Page Viewer webpart and switch from Web Page to Folder. You can the specify the folder you want to display in the Link.