> retrieve the currently applied discount by its ID…
you could do something like this

add_action('init', 'myprefix_discountids_applied');
function myprefix_discountids_applied(){
/***
session are per blog if multisite
***/
if(is_multisite()){
global $blog_id;
$session_key	= 'wppizza_cad_'.$blog_id;
}else{
$session_key	= 'wppizza_cad';
}	
$discount_ids = $_SESSION[$session_key]['discount'];
/*
now do something with the $discount_ids
*/	
}

>if I could determine if there are more than one discounts at play…
the above will tell you if there’s one or more at play (as there will be none, one, or many id’s in that array)

>apply your own logic…
i suppose i could add a filter somewhere, however, if you want to apply your own logic you could also simply add your own discount(s) depending on your logic, using the wppizza_fltr_discount filter – which is essentially what the plugin does – along these lines

add_filter('wppizza_fltr_discount', 'myprefix_apply_discounts',10, 3);
function myprefix_apply_discounts($discountvalue, $session_items, $order_parameters){
/* alter the current discount value as required */
return $discountvalue;
}

>So It seems that for some reason that a id 0…
what happens if you duplicate the one with id 0 and subsequently delete the one with ID 0 ?
(there *might* be an empty() check somewhere – which would also return true if the id == 0 – that should be isset() instead ) ?