In family sharing, can non-organizers make purchases with their own credit card? And will those purchases be private or shared?
Non-organizers cannot make purchases with a credit card separate than the account owner.
However, gift card credit is kept separate for each account. If a non-organizer loads a gift card, that non-organizer's purchases will come from that balance, while the other family sharing members' purchases will not.
No, if you want to make purchases with a personal payment method then a separate Apple ID will need to be created or Family Sharing left.