Hi, our kid's camera is rechargeable with a 1200mAh battery. 

Yes you can. In fact that is what I am doing right now. The one that came with the telescope was alright but the camera tripod I have is a Polaroid and works much better. 

Yes, it comes with a mount which is a plastic pipe with a pivot at the base. I'm sure you could mount the station itself on the same size pipe. The hardest thing would be getting it level. I'm not sure what diameter the pipe is but I would guess the outside diameter is around 1 in. The pipe in the picture is part of the base, and the unit sits over the end of the pipe. Hope this answers your question. 

Don't think so just put up a longer pole and take some hose claps and strap to the longer pole two should be more than enough I screwed mine to the peak of the house some time you can't get perfect north south pole is a good deal 

You can put it on a pole. Mine is on a 30ft pole. It works really great. Just make sure that it is not around a lot of trees. It can change some of the sensors like the wind speed and direction. And I found the first pole I had it on. In the wind, the pole wobble a little. So it effected the wind speed a little bit. So I used a little sturdier Pole and guide wire it. It did the trick.