As the stabilizer got a USB female port things are lot easier. Let me break your question into these two:
In order to use your Android device as a live preview device you need a capture card.
To view what you captured from the camera, you need an application for that.
Re: GoPro Hero4 Black edition has Wi-Fi as in the specs though some cameras lack in Wi-Fi. If you have Wi-Fi you don't need the equipment, you just need the GoPro app on your phone, and it will show you the moments you captured.
Let me answer.
You need an OTG cable with a Capture card for live-streaming. You can refer to the link for purchasing the capture card. Check this link for the video.
There is no possible way to view what you have captured unless you are connected via Wi-Fi or via the USB to PC.
You can try out connecting the camera to the phone via the OTG cable, you need a USB Male-to-Male cable for that.
Recommended Answer: Use an FPV (First-person view) cable for live streaming, easy and fast. You can find all the info related to it here.
Hope this helps. Good day!