Three Car / Insurance Questions

[IdealFugacity]

I will be graduating in late May. For my job, I will be moving for 12 months [duration of apartment lease] to Connecticut.

Question 1: Is it possible that by buying a car in late may / early June in New Jersey I will incur some kind of extra sales tax charge from Connecticut?

Questions 2/3 :
I have heard car insurance is cheaper in CT than NJ. Is this true?

Do I have to change my permanent address from my home state (NJ) to which I will be returning in 12 months time (albeit a different county as I will now be living on my own for my job in a different part of the state, whereas my current perm. address is my parents' house) in order to get CT car insurance rates?

bonus question: Is there anything (else) it would make sense to change residency for 1 year and then change it back to NJ next summer?

[Karmic]

1) laws vary
2) no idea
3) yes
bonus) state income taxes.