When most people talk about the Bubonic Plague, they think of the Black Death. But there have been a few more instances of the Plague causing mass death in Europe, such as it wiping out up to half the population of the Byzantine Empire in the 500's, AD, and being linked to the plague that nearly wiped out the population of Athens when they were being sieged by Sparta during the Pellopenesian war. Why do you think it came so many times, and each and every time just vanished all of a sudden?
Diseases mutate. They will find a way past vaccines and they never really disappear. If conditions are correct, ie lack of proper hygiene and medicine, obscure diseases surface that we'd assume are long gone. Tuberculosis is an example of this, which still flares up in 3rd world countries. The bubonic plague follows the same fate, and even appeared in India recently. You can never fully stamp out a disease. I'm assuming it vanishes so suddenly because everybody is dead and there is nobody else to infect as a result of it.
This is pretty much correct. I'd guess it vanishes quickly because of a mix of factors. Decreased population means decreased population density, this would make it harder for the disease to spread. Also, there are those who survived the disease, they're now immune to it, plus you have to factor in those who were immune from the get go.
Same symptoms. Must be same thing. Impossible to have originated from the amount of people living in enclosed area's or the literal shit building up in the streets. Or perhaps the total lack of sanitation in church holy water . In all three of the situations you sited there as a reason a disease to create itself amongst the filth of old society.