I'm 19 and at University! YABU
I was also state schooled but I have no idea why you think education has anything to do with an interest in politics. i have friends at Uni who are from very prestigious private schools and they couldn't give a jot about politics. On the other hand, I know plenty of state school kids who love it- one of my closest "state" friends is running for Councillor.
As for the rest of your post, I can see your niece's side of the things.
The dust comment, for example, was probably a throw away comment and was not intended to be rude. I imagine she simply said "oh it's probably itching because of the dust". I doubt she was commenting on the state of the house or anything. Most 19 year olds wouldn't even notice or think about that kind of thing.
I don't know why you were expecting a financial contribution when it was only one weekend and she is family. I think it's nice that she bought you some taramasalata. How did she "behave" as if she'd contributed majorly to the household? Feels like you are imagining what she is thinking.
I also think that she was probably trying to be friendly and entertaining by telling you about her boyfriend. I agree that it was probably inappropriate for the children to here but this was probably due to ignorance rather than deliberate rudeness. Just calmly say "not in front of the kids!" or something.
As for the washing- If I stayed at someone's house I would find it presumptuous just to use the washing machine by myself. I'd at least ask about it to make sure it's okay. As someone said above, I wouldn't want to make myself at home too much- that would seem ruder!
All fairly normal stuff in my opinion. Of course, I don't know the entire situation and it's impossible to know how she was behaving from a short post. Just thought I'd offer the opposite perspective...