Yes, if you put a default.aspx page in a folder (physical or virtual) then you won't need to use the file name.  If you have control of the server then you could even just create virtual folders that point back to the root.

You don't even need it to re-direct because the Url Rewriter will take care of it before it even actually gets to the file.

No need to log anything in Gemini. 

Using just a folder name is not something that can be accomplished inside the application alone.  You have to have access to IIS to map another extension (or all extensions), or create a virtual folder, or access to the root of the website to create a physical folder.