The display of the date is set by <?php the_time('F jS, Y') ?> in some files of the theme. As there are many ways to format a time and date display please check here how to change:
http://codex.wordpress.org/Template_Tags/the_time
In German themes I use sometimes: <?php the_time('d.m.y') ?> to display: 03.12.09
The "drop-down list" you talk about, do you mean the posts coming below the 'Browse Categories' section? This I would call the front-list as it is in a div id="front-list"
This front-list shows you by default all posts older than the four posts you have in the slider. You could start to include or exclude categories there, BUT this is the index of your site and excluded categories will be excluded on subsequent pages too. To make pagination work on a setup like this is quite difficult.
the_excerpt: in the slider (headslider.php) I use as replacement for the_excerpt this:
<p><?php the_content_rss('', TRUE, '', 30); ?><a href="<?php the_permalink() ?>" >read more</a></p>
so if for example you replace <?php the_excerpt(); ?> in line 45 of index.php with the line above, the first two post in front-list will show 30 words and a 'read more' link.
Changing the number 30 in that line to 40 will give you 40 words..