- Do you have the Apple TV box? If so, which model? Identify your Apple TV model - Apple Support. The Apple TV box (4th generation or later) supports installing apps from the on-device App Store only. Other methods are not available.
- The Apple TV app on third party devices does not allow installing Apple TV apps. Those apps are for the hardware device only. Instead, install apps as offered by the third party device manufacturer.
- There are no web apps to add for the tv.apple.com website for computer/mobile users. That site is for Apple TV+ content only.

For your second question,
See here for supported payment methods by country: Payment methods that you can use with your Apple ID - Apple Support.
Users would link a payment method to their Apple ID account, and then all purchases on that account will be charged to the aforementioned payment method. Add a payment method to your Apple ID - Apple Support. The payment method must be issued in the country that matches the country for your Apple ID account (Italian account, then also an Italian card). Subscription services require a payment method that can be charged automatically and periodically.
If needed, you can add money to the account as a form of store credit, from bank transfer or gift card.
Add money to your Apple Account balance - Apple Support
Check your Apple Account balance - Apple Support