Duel citizenship is not forbidden in the United States. There is no reason that this would be impossible. Wikipedia has a page on that (United_States_nationality_law#Dual_citizenship)
no you can not. You must take tests and live in America for about 3-5 years. It doesn't matter if you Mary an American citizen or not you have to do this. And i think you have to do some other things...
No, you don't automatically become an American citazen if your child is born in America. Actually you can be deported at any time to the government you came from. All because you filed a form...