I can't update my Apps, or download Free ones. Also when I go into Settings there isn't a None option for payment options.
I tried to enter my credit card but it says "Your payment method was declined"
My iPhone model is an iPhone 5c.
I would start with Apple support - https://getsupport.apple.com
Choose billing support in the web page or see if there is a phone number to get human support. If you exhaust your banking cards, then you might need to contact your bank to ensure your card details are correct so you enter them correctly on Apple’s site.
This thread explains how to edit AppleID information to match what your bank reports. Verification required