Wow being a graduate student is closed-shop in the US?! That’s crazy I never knew that. How does that square with academic and political freedom? A student who researches union abuse must join and fund a union!
Depends on the state and the public/private designation of the university. There is also the (mostly unanswered in the courts) question of whether private university graduate students are primarily employees or students. Read up on the kerfuffles at NYU and Columbia University to see how gnarly this all gets.
It's worth noting that graduate students were not able to unionize until recently at many private universities in the US. Even though they now can legally unionize, many remain unionless for one reason or another.