A:AnswerAccording to the manual the batteries can last up to 2 years. And they are not rechargeable, but they do come with a charging port if you decide to buy rechargeable batteries. Which isn't a problem since they are a simply 2 AAA batteries.
A:AnswerHave not used in such cold clime but have experienced reduced battery life in cold weather so you will likely need to replace your battery more often
A:AnswerReasonably, around 8-12 months with regular use. If you use the live cam feature or take still pictures a lot it will drain the battery more, as well as the intensity of the night vision, sensitivity of the night vision, and the duration of video recording.