Cannot Reset Security Questions

I believe your only option now is to try to upgrade to Apple's 2 Factor Authentication.

Assuming your are signed in to your phone using the same Apple ID.

https://support.apple.com/en-ca/HT204915

there is a contact link.

Apple ID Support

Apple ID Support (2) 

Apple Support by e-mail or chat    Work through the screens to get a chat option.    

Apple Support using Twitter

Or fill out and submit this form.          The form is for iTunes, but it will get passed to the ID Support section.