How to verify account without a credit card

That seems to be a scam/phishing email. Apple won't send you an email/text telling you your account is disabled/restricted  or will be disabled/restricted. You will find out the next time you try to log in somewhere.

Apple will always address you by your name or the name they have on file for you, not Dear Customer, Dear Client or by using your e-mail address.  The e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more. Apple e-mails will never contain an attachment. Apple will never request personal information by email such as Social Security numbers, your Mother’s maiden name or full credit card numbers .

The only exception to the above I have noticed is if you order something from the Apple Store (apple.com), your receipt will be addressed to Dear Apple Customer. That is a receipt for a purchase you initiated.

Avoid phishing emails, fake ‘virus‘ alerts, phony support calls, and other scams.   

Identifying legitimate emails from the iTunes Store.     

Send the e-mail to Apple as an attachment to a new e-mail before deleting it. You can forward as an attachment by going to Mail/Message/Forward as attachment. Or control - click on the email and select Forward as attachment. Make sure you send it as an attachment to a new email. If you just forward it, it will probably be rejected. You won’t receive a response.

reportphishing@apple.com

It is hard to tell what all is going on given what you have said. Start here in trying to solve your problem.

Check your device list to see if there is a device signed in that you don't recognize using Check your Apple ID device list to see where you're signed in https://support.apple.com/en-us/HT205064 Remove a device that shouldn't be signed in using the steps in the link. 

For safety, change your password using Change your Apple ID password

https://support.apple.com/en-us/HT201355

Here is What to do before or after you change your Apple ID or password https://support.apple.com/en-us/HT204071

If necessary, contact Apple ID Support.

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (Link doesn’t always load)  

Get Support          Work through the screens to get a chat option. 

https://twitter.com/AppleSupport

Or fill out and submit  iTunes Store - Contact Us - Official Apple Support  The form is for iTunes, but will get passed to the ID Support section. 

From the article below. 

Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.

Security and your Apple ID - Apple Support.