Also, if you moved to another country but you still have valid payment methods in the USA, there´s no need to change anything in your profile.
But, if you move to another country and no longer have access to payments methods with billing address in the USA you will have to change the payment and billing info on your account.
If you are looking to buy pre-paid cards for membership or Microsoft Points, try www.amazon.com. Remember to buy the cards that says Digital Delivery, as these are the ones that you received your code via e-mail.
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You will need to contact Xbox Support, to migrate your account to the new country. This process can take up to 6 weeks and you might loose some features (when they aren't available in the new country) and you will need a physicall address in the new country.