A. Not exactly, Term policies' rates don't vary a lot across different states, but depending on which state you are in, rates may be slightly different, even you have the same coverage and same term. So if possible, for example, your home is in one state but work in another state, you should check both state's rates and pick one that is favorable to you.
Once a policy is activated in a state, it's still valid even you move to another state.