Q: How do I reset my additional security questions so a new device can be added?

From a Kappy  post

The Three Best Alternatives for Security Questions and Rescue Mail

   1. Use Apple's Express Lane.

Go to https://expresslane.apple.com ; click 'See all products and services' at the

bottom of the page. In the next page click 'More Products and Services, then

'Apple ID'. In the next page select 'Other Apple ID Topics' then 'Forgotten Apple

ID security questions' and click 'Continue'. Please be patient waiting for the return

phone call. It will come in time depending on how heavily the servers are being hit.

2.  Call Apple Support in your country: Customer Service: Contact Apple support.

3.  Rescue email address and how to reset Apple ID security questions.

A substitute for using the security questions is to use 2-step verification:

  Two-step verification FAQ Get answers to frequently asked questions about two-step verification for Apple ID.