Who is the Organizer of the family sharing group?
You say you can log into the -presumably- Organizer's account but, "I can not change anything there either." More details about that would help. Maybe? -->
To find out how to remove a payment method, or if you can't remove your last payment method or use no payment method with your Apple ID, read this article --> Remove a payment method from your Apple ID - Apple Support
- Ongoing subscriptions and Family Sharing organizers must always have a payment method present. To edit the cards used for those you may need to first add the new card and make it the primary payment method before removing the old card ( If you need to change or update your Apple ID payment method - Apple Support ).
This document explains how to add a payment method to your Apple ID on a Mac, Apple mobile devices, or PC. Click here --> Add a payment method to your Apple ID - Apple Support
You may find the technical requirements for a payment method in the Organizer's name in the end mandate you disband the entire family sharing group and start it again with a new organizer:
Leave Family Sharing - Apple Support --> Leave Family Sharing - Apple Support
Set up Family Sharing - Apple Support --> Set up Family Sharing - Apple Support
From: Hi, how do I make me to family organizer,… - Apple Community
"If there are children under 13 years old, the new organizer needs to leave the existing family, set up the new family, and then the under 13 years old children can be transferred to the new family. Then disband the old family and join the new family."
Move a child to another group using Family Sharing ---> Move a child to another group using Family Sharing - Apple Support