Lots of SQL queries

Delete post/page revisions and that will reduce queries as well as the overall size of the DB. Run this in phpmyadmin (backup the DB first):

DELETE a,b,c
FROM wp_posts a
LEFT JOIN wp_term_relationships b ON (a.ID = b.object_id)
LEFT JOIN wp_postmeta c ON (a.ID = c.post_id)
WHERE a.post_type="revision"

Change table prefix above if needed. And run optimize from phpmyadmin afterward.

Add this to wp-config.php to prevent revisions from accumulating again:

define ('WP_POST_REVISIONS', 0);

See http://codex.wordpress.org/Editing_wp-config.php#Post_Revisions

And use that plugin pointed out above to see what else is querying the DB.