(why, oh why, do I get wrapped up in these kinds of conversations??? about how one would play a Jewish vampire character in a role-playing game set in Antioch at the time of the first crusade ...and having noted that the first person to respond is a rabbi of our acquaintance, I clearly just had to chime in:)
Sure, she can be a vampire who's a Jew--just not one who's an entirely halachically observant & consistent one--a description that's rare enough even in the non-undead Jewish community. ;) Even at the time of the First Crusade I'm sure there were a good number of Jews in Antioch who were eating things the rabbis wouldn't approve of (and drinking wine they wouldn't approve of, and sleeping with people they wouldn't approve of...). So she's no worse off than many others who keep some or even most of their community's norms but fall short in some areas.
On points that others have raised below or on the other thread:
I'm not up on all the vampire lore, but especially if vampires don't have to have died to be undead, I'm not convinced that halacha wouldn't apply to her character: can't you become a vampire by being bitten by one (without necessarily dying?)--and then you won't die, as long as you follow the, er, halachos of vampire survival re: drinking blood as needed, staying out of the sun, keeping wooden stakes out of your heart, and avoiding garlic and crosses [if you're a vampire in a Christian context]?
If vampires aren't the agents of the Devil/sitra achara (Other Side), and are just another category of being (maybe their cruciphobia is socially/culturally conditioned?), then I don't think she'd necessarily react badly to or be repelled by Jewish holy objects like a Sefer Torah -- though the mikvah-water ideas are interesting, either as atonement/purification option (I like it! very consistent with the general rabbinic/normative halachic approach to niddah as well as to its Biblical precendents re: body-fluid-boundary-disruption-rectification for women [re: vaginal/uterine blood] and men [re: seminal emissions] and both [re: "leprosy" problems]) or as thing-to-avoid (which picks up on the Christian-holy-water-avoidance aspect as well as on the Wicked Witch of the West "I'm melting!" aspect...though neither one is very Jewish!).
If she can subsist on blood from kosher animals, and/or can drink the blood of other humans when necessary for her survival without killing them and with their permission (is this possible, without turning them into vampires? is turning someone vampire, even if they say they don't mind, a violation of halacha because it's doing them harm--or could it be doing them a favor?), then I would think that doing so would be halachically permissable under the principle of pikuach nefesh, preserving life -- though the question again arises, then, of whether a vampire has "life" and whether the character's nefesh (soul, "breath of life") has been eliminated or endangered morally/ethically/spiritually by her becoming a vampire. My initial reaction is to think that she does have "life," albeit a different kind from that of most adult Jews who are bound by halachah. But if this is also the case for others in special conditions (e.g., someone in a permanent vegetative state or coma), for whom the ordinary strictures of halacha are abrogated when necessary to preserve their life, then I don't see why a Jewish vampire wouldn't be halachically empowered to drink the blood of kosher animals (as you say, preferably after shechting them herself, or making good friends with a local shochet who can get her what she needs) when necessary. And I'd think that if she's a person (even a vampiric one), she's still got a nefesh/soul. But I wouldn't pretend to know how the vampire lore that comes from Christian (or Christianized, even if from pagan folkloric sources) contexts fits or doesn't fit with concepts from Jewish tradition on the soul, life, etc. Besides the Golem (which was never living to begin with), ghosts (which presumably have no physical bodies and are definitely dead first rather than immortal "undead"), dybbuks (which inhabit the bodies of others but otherwise have no physical bodies of their own), and demons (which may take physical form but were never human to begin with), does Jewish tradition have any physically-concrete immortal/returned-from-the-dead/undead human beings? Vampires, zombies, unnaturally long-lived individuals (besides Methusaleh and other folks early in the book of Genesis, for whom it was presumably natural to have such a long lifespan--plus Serach bat Asher,) -- have we got any of those in our folklore or legends?
The wonderful French Jewish comics artist Joann Sfar has a series called Petit Vampire (Little Vampire)--and whether or not his little vampire is Jewish, one of his friends definitely is Jewish, and has the following conversation with the Flying Dutchman:
"I was kinda hoping you'd make me swear on a skull or something."
--"You want to swear a pirate's oath? All right."
"I swear to devote my life to protecting the dead and keeping their memory. And if I break my word, may a thousand curses befall me."
--"Now do the sign of the cross."
"No. I can't do that."
--"It would give more strength to your oath."
"But I'm Jewish, Captain. The cross doesn't mean much to me."
--"Do the sign of the star in that case."
"We don't do that either. And I don't believe much in God. 'Cause my parents are dead."
--"You're a bit young to believe in nothing."
"Well, maybe he exists, Captain, but after what he did to me, I don't feel like I owe him anything."
--"You should think about all that some more. Sad times often open miraculous doorways."