To see how to 'Get a verification code and sign in with two-factor authentication', click here --> https://support.apple.com/HT204974
If too many codes get sent to your trusted device then from your post and others like it, it sounds like Apple has a limit to the number of codes it will send, presumably to deter misuse. It could be that somebody was trying to get into your account and the two factor authentication system eventually closed the door on them trying, but unfortunately you too?
Click on this link "If you think your Apple ID has been compromised" --> https://support.apple.com/HT204145
As for the "account unavailable" message, that is a relatively new one to me and my only suggestion would be to contact Apple about it:
Contact Apple. Click here --> https://support.apple.com/choose-country-region Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.
or:
Contact Apple for support and service --> "See a list of Apple phone numbers around the world."
Click here --> https://support.apple.com/HT201232
Contact Apple for help with Apple ID account security - https://support.apple.com/HT204169 "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues."