So, a likely scenario is: a new virus appeared, it swept through the population, caused serious disease, a bunch of people died, the survivors had better resistance to it, it settled as a mostly innocuous thing (such as the common cold) or disappeared completely, and the next generations remembered it as "the plague of emperor Fancy Pants" or something.
Yes. But then again they didn’t start out as endemic virus but as a pandemic one. They probably wrecked a lot of havoc before becoming just a cold. Mayas and Aztecs can tell.