>On the settings page
I assume you are referring to the *order* settings page

>Can each menu item specify whether a delivery charge will be applied or not?
not natively in the plugin, however, there is the following filter you could use to substract the delivery charge if a particular item (let’s say with id 5) is in the cart
I also assume you are using “Delivery Charges per item” in the settings here

So, something like this (not tested, mileage will vary, but should give you an idea):

add_filter('wppizza_fltr_delivery_charges', 'my_prefix_delivery_charges_filter', 10, 3);
function my_prefix_delivery_charges_filter($delivery_charges, $cart_items, $general_parameters){
global $wppizza_options;
/* current set delivery charges per item */
$dcpi = $wppizza_options['order_settings']['delivery_charge_per_item'];
$reduce_delivery_charges = 0;
foreach($cart_items as $items){
foreach($items as $item){
if($item['post_id'] == 5 ){
$reduce_delivery_charges += $dcpi;	
}
}
}
/* substract */
$delivery_charges = $delivery_charges-$reduce_delivery_charges;
return $delivery_charges;	
}