please consider creating a child theme http://codex.wordpress.org/Child_Themes in which to make the edits. don't edit Twenty Eleven directly, as it is important to have an unedited default theme in your wordpress installation. also, all direct edits will be overwritten with the next upgrade.
the top space is from the top margin in:
margin: 2em auto;
how to remove the page titles - 'Home', 'About', 'Blog' etc.
change to a custom menu - 'dashboard' 'appearance' 'menus'
or if you want to remove the whole menu, remove this whole section from header.php:
<nav id="access" role="navigation">
<h3 class="assistive-text"><?php _e( 'Main menu', 'twentyeleven' ); ?></h3>
<?php wp_nav_menu( array( 'theme_location' => 'primary' ) ); ?>
</nav><!-- #access -->