Ok, this is what I think: if we're talking about the mythological/folklore vampire, then they are a fictional creation of ancient superstition, literary creativity, and Hollywood sensationalism. They're supernatural beings. We have many offshoots of these beings in fiction -- for example, in Laurell K. Hamilton's Anita Black Vampire Hunter world, vampires are basically people with fangs, although in one book she talks about one of the characters dying for a time when the daylight came, but avoided the question as to how this was possible. However, in her stories, vampires can have children, although, due to the age of the sperm/eggs, those mortal children have the potential for some sort of disease (I forget what she called it). Again, this is a literary creation -- not real. Because of the supernatural element in all these stories, I'd say these vampires are undead -- various varieties of corpses animated by some supernatural power.
Now, as to real vamps -- they are alive. They have to eat regular food. I don't know if all of them can have children, although I'd never considered that before, although I find it an interesting question because I have had three miscarriages. I have one son, but he was born when I was still a teenager, before I began to feed on energy. Every pregnancy after that resulted in a spontaneous miscarriage.
Now...that may or may not be related to vampirism. It could be related to the massive amount of coffee I drink. It could also be related to RH factor, or tumors of the uterous -- any number of things. (Sorry; I don't mean to be graphic, but I want to make it clear that a correlation does not mean that one thing caused another).
