I strongly disagree with this. I think looking at the answers can be one of the best ways to learn. Also if you're learning something for the first time, you MUST look at the answers to know for sure that you are tackling the questions correctly. Even those that are good at maths will need to...
Even if you did report it they can't really do anything about it since there is no proof. They would probably just sit her down and question her, then she would deny it. So yeah, you're kinda screwed either way
Depends on where your interests lie. In my opinion chemistry is the best, however it is probably the most content heavy subject out of the ones you have listed as well...