"If you don't get any options to verify your identity, you can't reset your security questions at this time."
Uhhhh... okay. Would be so great if next steps'd be provided for people in this category.
Question marked as
contact Apple ID Support.
Apple Support by e-mail or chat Work through the screens to get a chat option.
Or fill out and submit this form. The form is for iTunes, but it 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.