A customer should only type in his local number, and the system should automatically prefix the number with the country code, which can be looked up by the client's country (in profile)
After a customer edits the phone number on file, there is no way for him to logically return back to the verification page. A method should be put in place to help the customer.
When a customer enters in their info and CREDIT CARD details in the checkout form then gets routed to the Phone Verification sytem; once the customer verifies their phone number it takes them back to ...
There should be a test api button so that you don't need to do a test sign up in order to test that the api is work and also to preview your sms message that will be sent out to the end user.