Thanks for using the Apple Support Communities. I understand you have a problem with updating your apps in the App Store including the free of charge apps and you aren’t sure how to resolve the problem. I understand the need to use your account and I will be more than glad to assist you with some additional information that can help.
First, I would like to offer you this article that gives you different methods of payment:
Payment methods that you can use in the iTunes Store, App Store, and iBooks Store
For more information on how to update your method of payment follow this article:
Change or remove your Apple ID payment information
Keep in mind that if there is currently an unpaid balance or pending charge on your account, you might not be able to make any purchases until you have provided a valid method of payment.
If your payment method has been rejected, this article will provide you more guidance on how to resolve the issue: If your payment method is declined, or you have a billing issue with a previous purchase in the iTunes Store
I hope this information helps you to resolve your issue.