I can't even add OR remove a payment method.

If you already tried (to no avail) all the steps provided in this support article:--> If you need to change or update your Apple ID payment method , I suggest that you contact iTunes Store Support Team directly, and explain your problem, using this specific link:--> https://getsupport.apple.com/?caller=ikb&PGF=PGF51002&category_id=SC0060&symptom_id=21084

(if you get no help, look at the bottom of the above link, where you can contact them using "chat" or "phone" options).

Regards

Giulio