Hope you're well today! Let's take a look at your concerns inline! :)
1- send a unique code automatically at the end of payment with paypal
That wouldn't be possible "out of the box", it would require a bit of custom code. If you're comfortable with coding, you could use one of the many action hooks the plugin provides to tie into the payment process so you can send something like that.
2- during the registration process of the clients, ask (trhough a custom field) the fiscal code or italian vat, plus name and address necessaries to send the invoice
MarketPress provides a "Special Instructions Field" where you can collect additional details during checkout.
Plus, the plugin will automatically store shipping details of registered users, to make future purchases easier for them.
Would that work for you?
3- send the invoice trough email automatically from the eshop at the end of payment
MarketPress doesn't send invoices currently, though it does send an order confirmation after purchase. Receipts would normally be sent through the payment gateway you use though.
Does that sound viable to you?
4- monthly payments trough paypal, for example 300$ payed in 10 times of 30$ monthly.
MarketPress doesn't provide recurring payment features currently. We may be looking into that with a future update (the developers are working on some rather exciting updates currently), though for now, it would be best to simply include a subscription button within a product's content if you wish to do subscriptions.
Given the subscription aspect and some of the other items you mentioned, I wonder if maybe our Membership plugin would work better for you?
Any questions on any of this, please feel free to ask. We're happy to help! :)