Q: can family share member buy with their own credit card or only with family organizer payment

Seemingly, no.

Family members can pay from own store credit / iTunes Card, but not by credit card.

Family purchases and payments - Apple Support

redwood 342 wrote:

 

I want to share movies with my family members but don't want them to buy things with my credit card and they don't want to. Is their default way of buying something their own credit card or is the default mine as the family organizer? Do they have to specifically choose to buy something as a family member?

If they are members of the Family Sharing group, they can buy and redeem iTunes gift cards so that they maintain a store credit balance on their own account.  When they make a purchase (other than a gift) it will go against their own store credit before hitting the Organizer's credit card.

It will be their responsibility to maintain sufficient credit.