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1. Is the modem I received automatically on wifi? - do you mean if it's already configured to provide internet once connected? If it is, then yes, given that the service is already installed.
Check this article: New Connection Setup Help
2. What is the modem Identifier that I should use ? - do you mean the WiFi network name that you'll use to connect? It is printed on the sticker of the modem/router, including the default password.
Let us know if you need further assistance.