Probably. It probably changes every day where you are right now
Yes it does
Yes if you are referring to your public IP. Unless you specify with you internet provider you want a Static IP.
Your private IP much like you public IP is most likely dynamic also. Unless when you setup up your network you set if for static, in which case it will not change, even if you move.
Yes, it most certainly does
yes because you go to a new area and it changes
Most computers these days have dynamic IP addresses that change fairly frequently without their owners even knowing about it. If you have a static IP address (you'd know it if you did) and you stayed with the same ISP when you moved, you might be able to keep it, but otherwise it would change.
Just as an addendum to the other answers here – even with dynamic IP you could keep the same IP for a very long time as long as your computer or broadband router continues to renew the IP address when the lease expires.