Shopify app: adding a new shipping address via webhook
Here is the recipe:

create a Proxy in your App to accept incoming Ajax call from customer
create a form and button in customer liquid that submits to your Proxy
in the App Proxy, validate the call from Shopify and when valid, look for your form params. 
open the customer record with the ID of the customer you sent along with the form data, and add an address to their account

Done. Simple.
I'm planning to create a simple app using Django/Python that shows a nice button when installed by the store owner on user's account.
Clicking on that button should trigger a webhook request to our servers that would send back the generated shipping address for the user.
My questions:

Is it possible to create such button through shopify API or this something the store owner must manually add?
Is it possible to add a shipping address upon user request?

Thanks