Wireless Game Camera with Live Video Feed

I am not sure this is even possible but if so could anyone provide me some tips and pointers on where to start?

If it is possible could I also incorporate a trigger system for a trap that can be set off by pushing a button on my computer screen while watching the live video feed?

I'm not sure about the wireless video stream crap (is this is the right forum section?), but ...

... could I also incorporate a trigger system for a trap that can be set off by pushing a button on my computer screen ...?

What in the world do you mean by trap??
Are you installing a trap door in the floor??
You must have a touch screen if you have buttons on it?

Many vendors (even Harbor Freight) have wireless camera systems available.
Did you want to buy one or re-invent the wheel or exactly what did you have in mind?
And does it have to be a Game camera? (Is that for gaming or are you a hunter)?

If you leave out the video aspect of it then you can do this with any Arduino. Just have a wireless video camera.

It is much simpler if you just have a real button and use an Arduino with a wireless shield to talk to another similar system that will trigger the trap.