Your page-archives.php must be the same as archiveS.php - at least regarding its role and use.
[Good reading about the Template_Hierarchy]
In a normally made theme and a simple WP setup the result (read: the display of) the archives Page template should be something like this:
However, the archive.php is used to display listing of posts, e.g. for a category:
or a month:
Your original question was regarding a "category archive" - listing post in ONE category. This is done by WP just by clicking on a category name.
Now, if you wanted a separate sidebar for each category listing, you were supposed to use Category_Templates - a separate file for each category calling for its sidebar (or one category template file with a lot of conditional tags to call different sidebar for each category).
The easiest way to make a category template is to save archive.php or index.php as category.php (if a general template is the goal) or save it several times as category-xx.php where xx = the category's ID number.
After that you can edit teh template tags in it, e.g. replace the_content with the_excerpt and so on.
Simple, effective, clean.
Then with the plugin you set the number of posts shown and the order of them.
This is the normal way to do it.
Using Page templates... is the abnormal and complicated way.