Pull category slug, description and parent

i’m modifying a code from theme mimbo2.2

The original code that will display 3 categories which shows 1 recent post for each category:

<?php
$display_categories = array(5,6,7);
foreach ($display_categories as $category) { ?>

<div class="clearfloat">

<?php query_posts("showposts=1&cat=$category");
$wp_query->is_category = false;
$wp_query->is_archive = false;
$wp_query->is_home = true;
?>

<h3><a href="<?php echo get_category_link($category);?>"><?php
single_cat_title(); ?></a></h3>

<?php while (have_posts()) : the_post(); ?>

<?php
$values = get_post_custom_values("Image");
if (isset($values[0])) {
?>

<a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><img src="<?php bloginfo('template_url'); ?>/images/<?php $values = get_post_custom_values("Image"); echo $values[0]; ?>" alt="" /></a>

<?php } ?>

<a href="<?php the_permalink() ?>" rel="bookmark" class="title"><?php
the_title(); ?>&raquo;</a>

<?php the_excerpt(); ?>

<?php endwhile; ?>

</div>

<?php } ?>

From that code, I dont know what code to replace on the capitalize word below to display parent, slug and description of those listed category:

<?php
$display_categories = array(5,6,7);
foreach ($display_categories as $category) { ?>

<?php query_posts("showposts=1&cat=$category");
$wp_query->is_category = false;
$wp_query->is_archive = false;
$wp_query->is_home = true;
?>

<h3><a href="<?php echo get_category_link($category);?>"><?php
single_cat_title(); ?></a></h3>

<?php echo CATEGORY PARENT;?>

<?php echo CATEGORY SLUG;?>

<?php echo CATEGORY DESCRIPTION;?>

<?php while (have_posts()) : the_post(); ?>

<?php
$values = get_post_custom_values("Image");
if (isset($values[0])) {
?>

<a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><img src="<?php bloginfo('template_url'); ?>/images/<?php $values = get_post_custom_values("Image"); echo $values[0]; ?>" alt="" /></a>

<?php } ?>

<a href="<?php the_permalink() ?>" rel="bookmark" class="title"><?php
the_title(); ?>&raquo;</a>

<?php the_excerpt(); ?>

<?php endwhile; ?>

</div>

<?php } ?>

————————-

what i did so far:

1. I have no problem in pulling the category description:

i use this code: <?php echo category_description(‘$category’); ?>

2. but for the category parent and slug(nicename) i cant figure out how.

from wordpress codex (http://codex.wordpress.org/Template_Tags/get_category_parents), if I use this code:
<?php echo(get_category_parents($cat, TRUE, ‘ » ‘)); ?>

this will result to:
Internet » Blogging » WordPress »

How can I make it display Category Parent Only (eg. ‘Internet’)?

3. on pulling the category slug, i’m clueless.

thanks for the upcoming responses! any help would be greatly appreciated! =)