Q: Billing issue and unable to update apps

Are you on wifi or your cellular connection? try doing a hard reset on the phone, where you hold the power button and the home button for several seconds (ignore when it says slide to power off) just keep holding them both down until the phone shuts off, then turn the phone back on and try again using the other connection, so if you're on wifi now, do cellular after the hard reset. maybe try adding a different payment type and removing your current payment method....then add your first payment method back to apple pay.

What is the exact text of the message that you are getting ? If it's something along the lines of 'there was a problem with a previous purchase' then that means that iTunes wasn't able to collect the money for your last purchase and that you therefore owe iTunes for it - until that is paid off you won't be able to download anything else, including app updates, nor will you be able to remove your payment details from your account (you can only replace them) : Pay an unpaid balance in the iTunes Store - Apple Support

Or is it a different message ?