Try adding this in a plugin at the quoteit_bbcode_begin hook and tell me what it prints when viewing a thread with the bbcode in it. You can disable the plugin afterward.
PHP Code:
header('Content-type: text/plain');
die(print_r($quotebbcodeids, true));
I'm not sure how to handle the request to automatically add quotes when posting. The best way would probably be to add a the bbcode to the post before it gets processed, but you'll have to find the right hook. You can use this code to get a listbox with the categories:
PHP Code:
require_once(DIR . '/includes/functions_quoteit.php');
$listbox = fetch_quote_categories(false, $the_id_of_the_default_category);
You'll need to put that in another hook and then use $listbox where you want it to appear. Then when they submit the post, $_REQUEST['category'] will be an array containing the selected category id.