Hello.
The only thing that we sell that comes to mind would be our 4G connected camera here: https://www.securitycameraking.com/product/2mp-3-6mm-4g-elite-series-ip-bullet-camera-w-audio/ as it is our only 4G connected camera. We do not specialize in discrete cameras, we have a few hidden cameras or pinhole models but they are all wired cameras that require a physical connection for both power and data. We do not sell any battery powered cameras at all, so I do not have any recommendations I can make to you in that regard.
I encourage you to consider the fact that often discrete solutions are not necessarily the best solutions for every problem. Cameras can act as a deterrent to some of the activities you describe, and often discrete camera solutions are not designed for the types of deployments you describe. Night vision in particular is a big sticking point; if you want to see what's happening at night there needs to be some source of light and most cameras perform best using infrared. That means a visible source of light, be it a white light or the classic red infrared lamps.
If you're looking for something battery powered and quasi-discrete, you may want to look for something in the world of spy-cams or hunting cameras. If you're interested in something more permanent or are willing to consider a wired solution (perhaps part of a larger security system that covers your entire property) then we would have a better ability to service your needs.
Hope this gives you some launching points.