No, you need to check which battery model your camera is compatible with. 

Pretty sure it's water proof, Mine has been outside since I bought it. It works fine. 

After the mobile phone and the device are successfully connected, as long as the device is in the WiFi area where you are connected, your mobile phone can remotely view the device data through the APP as long as it is connected to the Internet. Please pay attention to ensure that you are using 2.4GHz WiFi when connecting, and the WiFi area where the device is located has a strong signal to avoid accidental disconnection due to weak signal. Hope this information is helpful to you. 

No, just open the deer camera's built-in WiFi via the controller and connect your mobile phone to it. then you can set the parameters of the game camera and download the recorded images & videos to your phone. 

No it has nothing to do with home wifi. It just links to your phone. I would call it more like Bluetooth rather than wifi