No unique IP with the Basic plan. The Max plan will have a (1) unique IP only if you use/activate SSL.
Also, the IP address that is assigned to any account whether it is a shared or unique IP address are static. They should not change.
Oh, yeah. I misinterpreted. Static they are. And as Ray said, they should not change, but that doesn't mean that an IP could not have to be changed for some reason.