The description can be inserted very simply with (begin php) echo category_description(); (end php) in your archives.php or category.php page.
You could alternatively make a custom category page, for example, if the category you want to customise is number 12, you copy the archive page, customise it and save it as category-12.php

I’m not sure I understand your second question - do you mean if there are two posts of the same name? In which case (I think) WordPress automatically adds -2 to the second duplicate post title or you could change your permalink structure to include the post number like the URL structure you see here on this very blog.

A couple of questions if you don’t mind as i like the idea of adding posts to categories and a small description to each category.

Is it easy to show the description if the theme i am using does not do this by default?

Would it not cause a duplicate content issue by using a category/post permalink structure?

Darren