I don't know what skin you are using but this looks a CSS issue. Find the CSS for the sidebar <h3> and edit it's margin and/or padding to suit

and in search, how to change the name of "root"

There's no easy way to change it :( but you can remove this option by changing 'true' to 'false' in the following code around the line 300

/*
 * Categories:
 */
if( $params['search_cat'] )
{
	$ChapterCache = & get_Cache( 'ChapterCache' );
	
	$Form->select_input_options(
			'cat',
			$ChapterCache->recurse_select( NULL, $Blog->ID, false, NULL, 1, $category_exclude ),
			$params['in_category']
		);
}