I have no remove or change payment options button in the settings location in the app store (as indicated by the tutorial) and I get an email that there is a problem with my credit card (which is true, because i have a new one). T

Sign in to your Apple ID account page and edit / update your Apple ID details.

https://appleid.apple.com

On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method.

Or -> Change, add or remove Apple ID payment methods

Change, add or remove Apple ID payment methods – Apple Support (UK)

• Add first the new card, then remove the old one.

If you update your payment method or add funds to your Apple ID balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.