I don't get any options to verify my identity, so I can't reset my security questions.

If you are being told there isn't enough information to reset them, contact Apple ID Support.

If you don't know the answers, if the steps in the article below don’t work, contact Apple ID Support, although based on multiple posts I have read, they will not help you recover the answers to your security questions.

 Apple ID - If you forgot the answers to your Apple ID security questions.      *

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 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. 

Apple Support schedule phone call. -

https://twitter.com/AppleSupport.  -

I'm in the same situation

1 - I can sign in. On the web, on iTunes, on iCloud... no issues with password

2 - I cannot do ANYTHING once logged in, including turning on 2FA. Asks me for Security Questions. I've tried MANY times, no luck.

3 - Resetting Security Questions and it "cannot verify my identity", but 0 options given

4 - Security code sent to "iPhone" and I've never ever owned an iPhone

COMPLETELY stuck here

Hi jensuwehaake,

We understand you're not able to reset your security questions. We see you were linked from the article "If you forgot the answers to your Apple ID security questions". As noted in the article, " If you don't get any options to verify your identity, you can't reset your security questions at this time."

Another option would be to try to turn on two-factor authentication. This allows access to the Apple ID without answering security questions:

Two-factor authentication for Apple ID

Hope this helps!

Have a great day.