Hi Trentzilla,
welcome to the Apple (user-to-user) Community.
Re: Why do I need a payment method for a free app/game?
Sorry that you have gone through such a difficult time recently with your financial information and account.
Seems Apple requires a payment method in your Apple ID account for the first time that you use the App Store or iTunes, even if you only download free apps / items. (If Apple gives a reason, I do not know where).
In many countries you can redeem an Apple Gift card, and use the balance as a payment method in your account:
Check the payment methods that Apple can accept in your country or region:
Payment methods that you can use with your Apple ID - Apple Support
If it can be used in your country or region, seems you can use the all-new Apple Gift Card for everything Apple:
products, accessories, services, and more.
Apple Gift Card - Apple
You might want to redeem a gift card to make it available for use:
How to redeem your Apple Gift Card or App Store & iTunes gift card - Apple Support
and
How to: Check your gift card balance - Apple Support
How to add an Apple ID payment method to your account:
Add a payment method to your Apple ID - Apple Support
How to delete an Apple ID payment method:
Remove a payment method from your Apple ID - Apple Support
How to change an Apple ID payment method:
If you need to change or update your Apple ID payment method - Apple Support
If needed: More info / support / contact options
Apple ID support / help website:
Apple ID - Official Apple Support
or
Subscriptions and Billing Website:
Subscriptions and Billing - Official Apple Support
All the best :-)