No, it doesn't include internet and telephone calls.
Your host can charge you $10- $15 per week for internet access. The internet access provided will include a decent connection and download quota. However, please understand that many Internet Service Providers do not allow unlimited downloads. Also, copyright law is enforced in Australia, so do not download movies or games. The internet access provided by your host is for email, study and communication with your family and friends in your home country.
For telephone calls, you should use your own mobile to make and receive calls. However, if you want to use the home (landline) phone to make a local call, you should pay your host 40 - 50 cents per local call.