I know exactly how you are feeling. The one thing that I disliked was the fact that Nottingham wouldn't budge until I made them my firm choice.
If I were you I would call Nottingham Hospitality, and ask them about Broadgate Park. I found that speaking to them on the phone took me a lot further than emails. Sometimes they didn't even reply. The chances of finding a place to live depends on the choice of room you are looking for. If you want a studio, then the ones allocated to undergrads have already been taken, or so they told me. You might get a chance to live with post graduates if that isn't an issue for you.
I don't know about emailing Manchester to release you, but once again, I would call them rather than email. You can get faster and specific answers.
When it comes down to studies, Nottingham is an amazing uni, and tends to be noted for its ranking. Then again, you need to think about your personal needs. Do you want to go to a place that you know is more lively than the other, has more arabs, and so forth...then that is Man. The opposite would be Nottingham of course. Still, I am sure there is tons to do in Nottingham. I haven't seen the place yet, but i've got great feedback. Also bare in mind Man. is more expensive than Nottingham.
Call in Nottingham, ask them when the final date to decide would be, considering you are an international student. Also make the accommodation people aware of the fact that you are an international student too.