It's mentioned several times that Anabelle's bearing is reminiscent of the Founding Families, and she's even met for the first time at one of their parties. She also seems to have some amount of money, given her high-level participation in both contests so far. I think a connection is very reasonable to assume.
That said, since she's unfamiliar to the other FF girls, it's probably a complicated situation. My guess would be she's the daughter of an excommunicated family member - probably a lower ranking one too, a distant cousin or nephew or whatever. Someone who had very little influence to begin with, did something that embarrassed the family, and was cut out.
It's hard to ascertain her motives. Assuming this is her situation, does she want back into the family? Does she want revenge on those who wronged her parent? Does she seek to change the unjust system entirely? These all seem largely too ambitious for her based on what we've seen, but we've also seen almost nothing of her so who knows.
Her request for a friend was certainly odd, though it's entirely possible she's a shrewd manipulator who's playing at being a clumsy ditz and trying to ingratiate herself with the newest and least experienced FF head. I think that's unlikely, but a possibility worth keeping in mind. Wouldn't be the first time a girl plotted behind our backs and ended up regretting it once they got in too deep.
