Re: Nemesis
Some of the other subjects I believe she should ahve studies include: Physics (for gadgets and knowledge on the natural world, tempreture, velocity etc), Philosophy (ethics, logic and I reckon she'll need this)**, economics (if she is running her family business empire).
**
And a suggestion: under a assumed name she goes on a pilgramage to the Shaolin Temple in China. They she learns an ancient martial art. Why do they help her is up to them, they have their reasons, and possibily to help her find peace after all is said and done.
During any combat she will need an inner focus and time clock that is boosted by spiritually and peace she learns from the temple. It will allow her to kick *ss and take names all that better. She would still avenge them and "hate" the crimials who took away her family but when she needs to find peace...she can, because of the Temple training. Otherwise I reckon the passion will eat her up and become uncontrolled and she will end up torturing herself.
Her vengence needs to be clear, something she can tap into when she needs to, but also to "let go" in situations when it is inappropriate (eg State dinners...and you know they will take advantage).
All my 2 cents, take what you want and discard the rest.