Yes, you can still get the Black Death ( also known as the bubonic plague). To treat it, doctors use antibiotics to soothe it. The last answer was incorrect. Don't believe him or her. Give me a trust...
One form of Bubonic Plague DOES cause skin discoloration- very dark purple that is almost black. Caused by blood coagulating under the skin, fingers, hands, etc. I suppose that "Purple Death" did not...
That depends on the country of the infected, and the superstitions surrounding the plague. Many would simply leave the bodies in the houses, since they were traditionally locked up to stop the plague...