You are logging into the account by tapping on it in Settings > iTunes & App Store on your iOS device or via the Store > View Account menu option on your computer's iTunes, not when trying to download something ? If when trying to download something then you probably won't get the 'none' option.
If you aren't getting the 'none' option : Why can’t I select None when I edit my Apple ID payment information? - Apple Support
When you say that aren't getting the option to turn auto-renewing off, do you mean that you have some auto-renewing subscriptions on your account but can't stop them renewing, or that you aren't seeing that section on your account (which would mean that you don't have any subscription being charged through iTunes) ?
If you have card details on your account then they need to be valid details for iTunes, if the card's details are not being accepted then you will get an error message when you try to download something (including app updates), it doesn't necessarily mean that you have any regular payments (e.g. auto-renewing subscriptions) on it and/or that you owe iTunes anything (if you did owe iTunes you would get a message about a 'problem with a previous purchase' when trying to download something, not about verifying card details).
For the card being declined, if you are trying to use a debit card then they no longer seem to be accepted in all countries, and even where they are it seems that not all work. For a card to have a chance of being accepted it needs to be registered to the same name and address (including format and spacing etc) that you have on your iTunes account, and have been issued by a bank in the country where you and your iTunes account are.