Hm, so could you look into your database, serendipity_images and see how the nun-viewable media is inserted there, and whiche file extension it says there? Maybe it is a problem because of the double file extension '.tar.zip' - maybe using '.tgz' should work?
About hiding certain categories: This is currently not possible, but in our 0.8 development branch we use smarty. You can there easily add some if-clauses to force certain categories not to display.
However, in that development branch it's even easier to develop a custom plugin. You can use the "entryproperties" plugin and add a property like "download entry". When publishing an entry you can fetch all entries which have that attribute and just display their content in a surrounding HTML page which is better suitable for your layout. You could also display each entry's content within a list item, so that it looks more like a download area.
I know this is not so very easy to achieve, but I don't know any other blogging-centric application which would make it easier. If that feature is important to you, you may want to look more into thte direction of a portal application like phpNuke or Drupal, which (I suppose) have integrated download areas.
But if you'd instead like to contribute such a plugin, I am most sure others could also use it!
Regards,
Garvin.