I'm not a huge sci-fi reader, so no - I based the name on the literal n-body problem (on how to predict the individual motions of gravitationally interacting celestial objects), but the (literal) three-body problem is a part of that bigger cluster, so you're not too far off.
Not yet. She's on my list. I'm reading too many books at the same time, so I don't know when I get to her yet. If your reviews are to be trusted, it's right down my alley.
I figured with your background you'd have a better insight into those aspects of her novels than I would.
I'm happy about any writer who doesn't use art as background decoration or pure reference. She seems genuinely invested in the topic, which is refreshing. Yet, I still only know excerpts.