Categories Template Assistance

Remove the cat parameter from your query and name your template file category.php

From the WordPress Codex on Template Hierarchy;

 1. category-{slug}.php - If the category's slug were news, WordPress would look for category-news.php
 2. category-{id}.php - If the category's ID were 6, WordPress would look for category-6.php
 3. category.php
 4. archive.php
 5. index.php

The above denotes the order in which WordPress searches for template files and if it finds one that exists in that hierarchy, it will be used as the template for said condition.

So in this case you want to use category.php to create a global category template.

Of course, you can get creative and do all manner of things to meet all manner of conditions but if your basic requirement is as you describe then the above will suffice.

Edit

Replace this:

<ul class="category-7">
    <?php $archive_query = new WP_Query('cat=7&showposts=1000');
    while ($archive_query->have_posts()) : $archive_query->the_post(); ?>
<li><a href="https://wordpress.stackexchange.com/questions/76580/<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a></li>
    <?php endwhile; ?>
</ul>

…with this:

<ul class="category-7">
    <?php while ( have_posts()) : the_post(); ?>
<li><a href="https://wordpress.stackexchange.com/questions/76580/<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a></li>
    <?php endwhile; ?>
</ul>