Yes, they do. They may not sweat and such as humans do, but they can get dirty just like everyone/everything else in this world.
yes but not all the time
There were showers in the 1850s, so yeah.
showers were showers, normal inmates would only have one shower during their stay. But you might be confused with the fake shower heads that were in the gas chambers of extermination camps. They were not showers.
There is nothing bad about baths! I think that only little kids should take baths though! And adults and teenagers should take showers!
They used springs for showers and they used wholes in dead trees as a toilet
No. that would be disgusting
Wouldn't the heat make them burn.
Vampires don't usually take baths, as the effect of the evaporating water on their skin reduces the pleasure of drinking human blood. Most vampires take showers in bathrooms they have in their houses.
Koalas do not take showers.
People take showers to wash away dirt, sweat, oil, and body odor.
It is possible to take cold showers during the winter, though it may be uncomfortable.
no
yes
yes
No 
As vampires are purely fictional the only way is to take the authors word for it.
They're just vampires. Simple as.