My opinions on the questions presented:

1. Such a mix is never mentioned in the book. There are several reasons that such a thing would probably be very twisted, the slave-like relationship with wizards, the differences in physicality and mentality, among other things... but if twisted is what your going for that's another matter!(oh look we are talking about sex again!)

I'm certain that a mixed child would not be considered pure-blood. It is made clear in the books that Voldemort and his death eaters view other non-human magical races as inferior, and to be exterminated or enslaved. (Remember the scandal of having a Centaur teach in the school? The headmistress of Beauxbatons being offended when Hagrid suggested she was part Giant? there were a few examples.)

2. I think once she found out a wizard she read all her textbooks before the semester started. She is super smart and talented so she was able to pull it off before school. I think that is what they say that in the books. I think they also say that no one is supposed to learn magic really before they start school, but it happens in the wizard culture anyway and no one really enforces it as an actual rule. 

But we can do what we want :D