A SQL Azure DB is a child resource of a SQL Azure Server, and hence its lifecycle is tied to the parent. If you want to use an existing SQL Azure Server, you have two choices:
Apply the WebSiteSQLDatabase template to the Resource Group (RG) that already houses the existing SQL Azure Server.
You will have to use the same values in the Template that the SQL Azure Server is already deployed with. (You can GET the details of the said Server).
This will deploy the net new SQL Azure DB into the existing SQL Azure Server.
This will also deploy the Website and the related resources in the same RG.
Author Template number 1 with just a SQL Azure Server and a SQL Azure DB and apply to the existing RG with the said server.
Author Template number 2 with the Website and related resources, and apply to a net new RG.
Pass the SQL Azure DB connection string from template number 1 as a Parameter input into the template number 2.
Wrt your question about the "allowed ip addresses". These is set on "Firewall Rules" object which is a child on the SQL Azure Server. So which ever approach you go with from above, you can add the IP's under the "Firewall Rules" of that server in the template.