Anna seems to be a bit of a Faux Action Girl but if you think about it, she's a woman in Victorian society so it's likely the men in her family did most of the fighting and Anna was most likely trained to defend herself but not given as many opportunities to do so. Most likely she started fighting full time when her father disappeared but she still had her brother to help her. It makes her Crowning Moment of Awesome where she stakes Aleera that much better.
The Valerious family made a vow that they would never rest and enter Heaven until Dracula is dead. This is actually applied literally, which many of them misunderstand, believing they must be the ones to finally kill him. This is not actually the case. If Anna dies before Dracula, the curse still will be lifted if he were slain later by another... because the last Valerious would actually be Dracula himself. He was the son of the Valerious who initially made the vow, thus his death would still allow the family to rest as the vow would now be applicable to him as the only Valerious left to fufill it.
...That makes sense. But you do remember that Werewolf!Van Helsing had already killed Dracula by the time Anna dies, right?
I think quite simply, they misunderstood the vow. They believed that if they all died before Dracula did, they wouldn't ever enter Heaven... but the point is, they would regardless, even if it was only after Dracula died. If they died after Dracula died, same result, just sooner. Thus, when Anna died after Dracula, we see her and her ancestors entering Heaven at the end.
Dracula is the son of Valerious, one of Anna's ancestors, which means they are related. If that's the case, how can you justify the ballroomscene?
The same way you justify it between any two people of a very old village: distance (both genetic and, considering vampire sterility, social). On the other hand, you could justify it as Dracula being Dracula.
Minor point but: vampires in this movie aren't sterile, at least with eachother, andd the Immortal Procreation Clause doesn't apply. The plot itself revolves around Dracula and his brides having a lot of offspring that are born dead.