US "license plates" are different from UK "number plates." License plates do not follow the car. In fact, a car can have more than one license plate during it's lifetime. Since license plates are given out by the state, if a car goes from one state to another and is re-registered, it will receive a new plate. If you are really trying to figure that out, you have to consider that each state is like a quasi country. But it's really more "fluid" than that because in the States, we have antique plates if your car is over 20 or 25 years old. We have "vanity plates" which allow you to personalize your plate with your own "message" of 8 characters. Then some states allow a choice of plate that says you are a pet lover, a veteran, support a certain team, etc. So a car can can have had more than one plate even if the owner and state of registration doesn't change. Mine has. They are only, the best I figure because I've never really thought about it, a way for a cop to figure out who owns a vehicle and for the state to take more of your money. Each year, the registration (which the plate ultimately signifies) has to be renewed. In North Carolina, that means you have to put a sticker on your plate to signify it has been renewed.
In answer to your last question, There are different rules in each state. Usually, plates are issued by the sate but I know people with old MGs who registered their car as an antique and were issued antique plates but they mount a plate from the year of the car but they keep their antique plate under the seat of their car. I don't know how that actually works with the police but it's apparently not a problem.
That's probably a lot more than you wanted/needed to know but your local bureaucrat needs to know that you shouldn't expect a plate to be on the car when you get it from the States. If he or she needs to know that it was a legal car in the states, the Department of Motor Vehicles in the state where it came from should have a record of registration keyed on the VIN. With a Europa, that might be the 5 characters on the plate under the windshield or the "whole" number which includes the month and year of manufacture. A policeman might want to check the VIN of your car to check to see if it's stolen and he would check that plate under the windshield. It should line up with the registration (and thus the plate). I don't know if there is a problem if your registration has the complete VIN (manufacture date + serial number) which is not on the VIN plate under the windshield...
Whew!!! Hopefully that helps!