Since this phone arrived, it was connected to my wi-fi at home but doesn't show a wi-fi icon in the status bar at the top is this normal on this phone?
You should have a WiFi icon in the status bar if you are connected to a Wi-Fi network.
Are you sure that you are connected to a network? Go to settings > Wi-Fi to see what it says under your network. Perhaps you could upload a screenshot on this menu?
