Do you have to pay to change your IP to your router??

Router IP is "dynamically" assigned. For consumer level Ive never seen it change. I suspect if you trade in your router it will get a new dynamically assigned ip due to the MAC address change. I would call comcast customer service. In my region they are actually helpful, contrary to how they were several years ago.

I have never had to pay but when you think about it your ip is simply who ever is your internet provider but the best thing i would do is get a vpn if your want to keep your ip private

Not sure. Sorry.

I've never done that before.