first, congratulations to your Fulbright! I hope you'll enjoy your time over here in the US.
To the others who asked questions on the scholarship: I am a Fulbrighter from Germany, and from what I have heard from a lot of fellow Fulbrighters is, that the program differs by country. So I have heard that in many nations, the scholarship lasts for two years covering all costs (living costs according to the city you are located at; tuition fees; health insurance; the flight; etc.); in other countries (e.g. Germany) the scholarship covers only 1 year of studies (and is in the process of being changed again to a lump sum); a friend from Pakistan on the other hand receives 5 years of PhD-studies including living costs in NY; then, again, a fellow Fulbrighter from the Netherlands has received only (I believe) something like $12,000 as a lump sum. ... So the best way to find out what is the case in your country is by reading the websites of your regional fulbright office.
The 2-year home-rule applies for all fulbrighters; even if you married an American, there is almost no way of getting out of it. (In fact, the only way I heard to get around it, is to work as a diplomat.) I am doing at the moment a Masters, and I am about to apply for an econ-PhD for next year. So, it is possible to shift the 2-years home-rule a bit further down the road. After the studies, you also have the possibility to do an OPT (optional practical training) in the US of up to (I believe) 1 year. After your OPT, there is however no other way than going back home for the 2 years. (I have heard that for EU-citizens, the EU is fine and it does not need to be Germany specifically... not 100% sure about that, though).
The placement is done by the IIE after you hand in your list of preferred schools. However, in our case in Germany, it was possible to apply on your own to other schools, too. Since the IIE sends out only one application, there is a chance that you get rejected (in particular if it is a very competitive program you are trying to get in), and if there are no more open deadlines for new applications, you may even lose your Fulbright-scholarship since you couldn't get placed. (I heard of a guy over a mailing-list to whom that happened!) If you also apply to another schools on your own (as I did to have a backup), we needed to let our local Fulbright-commission know about it. If you want to enter a program that costs considerably more than the school which was chosen for you, you may need to contribute to the additional costs on your own (or with another scholarship from the school).
@Yaren: where did you finally apply to?