학비가 본교보다 많이 저렴할줄 알았는데 비슷한것 같던데요.

NYU alumn here, I dont know which options you have on your plate now but if you have plans to come over to the States, I'd definitely say Shanghai is NOT the campus you wanna go for.
And for your question of transferring:
Not many internal transfers are made from Shanghai to Washington Square