Hello, it's hard to say if a dog could push it, but it doesn't take an extraordinary amount of strength. We haven't tested this scenario yet but we can certainly look into this, thanks for the suggestion!
It just depends on how much you use it. It just takes 4 standard AA batteries.
This product is not waterproof and is intended for indoor use.
You probably could short term but I wouldn't leave it for long. The humidity in the fridge would most likely corrode the contacts and make the power drain quickly from the battery.
It comes with an anchor and screw in the package :)
It is 5" across
Yes! All you need is 4AA batteries, put it where you want it, and tap it on and off!