It’s worth noting that due to brilliant design decisions, the only way to put different tires on it is to replace the whole wheel. edit: apparently this part was not correct, my apologies for the misinformation
Yeah the rubber part gets replaced.
Correct the spare tyre is the wheel+tyre as you can't just swap the tyre on your own. And yeah rotating is just moving wheel+tyre to a new position on the car so the tyre gets a different wear pattern which helps it last longer.