How to move snapshot Azure SQL db from prod to dev on a recurring basis
You can use CREATE DATABASE AS COPY to create a snapshot of production database, and then use the same CREATE DATABASE AS COPY option to create databases for development environments using the snapshot database. All this can be automated using an Azure Runbook. The runbook can run with a SQL login with elevated privileges to accomplish all copy activities. 

CREATE DATABASE db_copy   
    AS COPY OF ozabzw7545.db_original ( SERVICE_OBJECTIVE = 'P2' );


Adopting Azure Web Apps may help you, because of their ability to override application settings and connection strings from within the Azure Portal. This way you could allow your developers or infrastructure admins to deploy new code to the Azure Web App without letting them even see the appSettings and Connection Strings that particular environment uses.

Visual Studio Team Services resource groups and Microsoft Release Management Agents may be very useful for you.