1. Is there a way to display all untagged posts? I tried taking the tag name out of the URL, and that just displays all posts.

global $DB;
$items_with_tags = $DB->get_col('SELECT itag_itm_ID FROM T_items__itemtag');

$items_without_tags = $DB->get_col('SELECT post_ID FROM T_items__item WHERE post_ID NOT IN ( '.implode( ',', $items_with_tags ).' )');

Once you get item IDs you can use ItemList and set_filters

$ItemList->set_filters( array(
    'post_ID_list' => implode( ',', $items_without_tags ),
) );

2. How can I get to the variable containing the table prefix? I assume it's out there somewhere, as it's in the config file and I was able to find other data in the config file (host name, database name, etc) under $DB, but I can't track down the table prefix.

Use T_ prefix in your queries, it will be automatically replaced with the real tables prefix

$DB->query('SELECT * FROM T_blogs');

The actual code will be

global $DB, $Blog;
	
	$items_with_tags = $DB->get_col('SELECT itag_itm_ID FROM T_items__itemtag');
	
	$items_without_tags = $DB->get_col('SELECT post_ID FROM T_items__item WHERE post_ID NOT IN ( '.implode( ',', $items_with_tags ).' )');

	// Create empty List:
	$ItemList = & new ItemList2( $Blog, NULL, NULL );

	// Filter list:
	$ItemList->set_filters( array(
			'post_ID_list' => implode( ',', $items_without_tags ),
		) );

	// Get ready for display (runs the query):
	$ItemList->display_init();

	if( $ItemList->result_num_rows )
	{
		while( $Item = & $ItemList->get_item() )
		{
			echo $Item->title.'<br />';
		}
	}

Ah-ha. And thank you for the impromptu lesson on how to use the built-in b2evo SQL functions, which was my next bit of work. :)