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 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. Although this is never touched on in the movie because Werewolf!Van Helsing had already killed Dracula by the time Anna died, it's likely there was never any race to defeat Dracula before Anna and Velkan died.
Igor turns out to be The Renfield to Dracula. In the original movies, Renfield and Fritz (the character mistakenly called Igor) were both played by the same actor, Dwight Frye.
Perhaps the original deal wasn't quite what it sounds like. Perhaps it was a kind of "Sold Your Soul To God" thing? Perhaps the deal was that once Dracula had been killed with the assistance of a Valerious, every member of the family would go to Heaven, regardless of their actions in life, just as a deal with the Devil might see you going to Hell. In the bible itself Jesus wasn't adverse to making deals in exchange for suffering (such as with James and John). Such a deal would indeed have risks in the light of failure.
Dracula is the son of Valerious, one of Anna's ancestors, which means they are related. Some viewers might be uncomfortable with him deciding to make her his bride (including, presumably, having his brood) with that in mind, even if they wouldn't really have much in common genetically given the large generational gap.