Hmm, well, here in the U.S. people are admitted to the bar by passing a state bar exam and fulfilling a few other dog and pony show requirements (a certification of your moral character being the most humorous of the lot). You pretty much need a J.D., which is a three year postgraduate degree, since no undergraduate course in the U.S. can prepare you for the life - although there are apparently alternatives. After you have that and jump where they say jump, you are pretty much in. People only really worry about the J.D. and the Bar exam, with both the last one and the rest of the requirements being part of the ABA racket more so than anything else.
I don't know about the residency stuff or whether you could practice without a green card (I'd think not, but I really don't know). I think I can say without need of research however, that practicing law will not fast track a green card application for you. Why should it really? We aren't in need of lawyers over here.