although there’s probably a case that can be made to perhaps do some scripting that would account for this, the fundamental problem from what i can see is as follows:

though your pages are translated , you are using the non-translated shortcode on these pages.

i.e on your IT page you are using [wppizza category='crepes' noheader='1' showadditives='0'] which works fine, as we know
however, on the EN translation your are ALSO using [wppizza category='crepes' noheader='1' showadditives='0'] where you should be using the shortcode that references the EN categories – that is [wppizza category='crepes-en' noheader='1' showadditives='0']
(note the category slug difference)

not using the associated slug will in effect result in the categories not existing for that language (in simple terms) which will throw these issues and therefore the plugin will not be able to add anything (categories are somewhat essential for all sort of things)

let me know if the above makes sense. (certainly fixes it when i do this here with your setup)

looking at your /wp-content/debug.log when (unsuccessfully) trying to add something to the cart myself here
https://www.pizzeriacarignano.it/en/order-online/crepes/
i get a Undefined offset:....../class.wppizza.categories.php on line 192

which leads me to believe it’s (perhaps – cannot be sure yet ) a non-translated category ?

can i ask you this as well please: are all categories that an item belongs to also available (and translated) for your other languages ? or maybe there’s an option in WPML that lets you enable/disable this ?
just trying to narrow things down . After all I do not know every single option available in WPML as I am not the developer of WPML of course

there are now some globally available and more versatile wrapper functions available
https://docs.wp-pizza.com/developers/?section=email-print-templates

“Warning from paypal custommer service” is also a misleading topic . nowhere in that email is anyone saying they are from paypal or paypal customer service (legally that would probably be misrepresentation or whatnot – i’m not a lawyer – and lead to jailterms if caught)

sure , if you give them access to your paypal account they will be “looking after your account” , but not in the way you want them to , i can assure you

Generally speaking though, if you are worried about things, contact paypal directly (and don’t reply to those emails, but literally pick up the phone or go to their website and contact them there)
Same applies to anything else along these lines; paypal , stripe or whatever other payment gateway or accounts you use/have

And last but not least: I really am the wrong person here to contact for this sort of thing. I am not a security researcher or advisor. Actions you take regarding emails you receive are really your responsibility.

The above is my take on things as I see it from the information you provided and I am happy to give you my thoughts on this
BUT, the security of your paypal (or any other) account lies with you. I am not responsible for the actions you do or do not take (Just want to make this clear)

thinking out loud for a sec. i wonder if this is actually down to something that changed in wordpress itself.
I am not going to spend too much time finding out if this is the case, however it is simply a matter of replacing (my end)

$first_term = get_the_terms($atts['id'], WPPIZZA_TAXONOMY); , which worked like that for years with
$first_term = wp_get_post_terms($atts['id'], WPPIZZA_TAXONOMY);

no, i don’t know either why the 1st doesnt seem to work anymore but the 2nd does. oh well

question:
how exactly are you generating the output of this page
/matsedill/shakes/
secondly, what happens if you use a default theme (like 2016 for example)

I’d need a link to the page in question really.
the above is/was really just guesswork on the info supplied

PS: the default $styles array is this

$styles = array();
$styles['ingrinfo'] 	= 'white-space: initial; margin: 3px; line-height: 130%;' ;
$styles['ingr_item'] 	= 'font-style: italic;' ;
$styles['ingrinfo'] 	= 'white-space: initial; margin: 3px 3px 3px 20px; line-height: 130%; font-size:85%;' ;
$styles['ingrgrp'] 	= 'white-space: initial; margin: 3px;line-height: 130%;' ;
$styles['ingrgrp_0'] 	= 'white-space: initial; margin: 3px;line-height: 130%; display:inline' ;
$styles['ingrgrp_1'] 	= 'white-space: initial; margin: 3px;line-height: 130%; margin-left: 15px' ;
$styles['ingrgrp_lbl'] 	= 'font-weight: bold; padding-right: 3px;' ;
$styles['comments'] 	= 'padding: 3px 0; font-size: 75%;' ;

wppizza menu items (just like normal WP posts) must be assigned to a category
if you do not set one – and when i add something in an update that deals with avoiding this warning – all that would happen is that i would force a category for you programatically (the first/top one in your wppizza categories list)
so you might as well select one that is most likely more appropriate i would think

hope that explains things somewhat