Why can I not use my card or verify it and when I do it says failed?

I had a similar problem, but my situation is possibly unique and might not help.

I have a UK based account, and a UK credit card, but I was trying to add my new details whilst on holiday in a different country.

I fixed this by contacting to a VPN, then adding my credit card via https://appleid.apple.com

Something else to consider, iPhones and iPads don't always transfer you to your card issuer to confirm your ID (I get a 'One Time Passcode' OTP SMS to me from my bank) and authorise the activity, so use the link above, (this is a relatively new step required by law in UK and Europe, possible others)

You can head to Settings -> Apple ID -> Payment and Shipping and then register your payment method there. If it fails there probably is a problem with your bank or card.