Don't worry about the large amount of questions as I'm happy to answer them
I'll number you questions going in order and give my response that way as I think it will be more logical and easier to understand. So here we go!
1) The city is fantastic and has something to offer to everyone, so if you're like me and prefer different things to do except nightclubbing then there is a vast range of theatres, cinemas, a few museums and other things to please everyone. If you're into the touristy things then you've got the whole robin hood thing going on, there's the oldest pub in Britain there too, plus you could always explore the Nottingham caves. Now if you are into the clubbing scene then the nightlife is very good with plenty of bars and clubs open every night and discounted rates for drink on certain nights depending where you are, so there literally is something for everyone.
2) I would say that people's opinion will vary on this question, but for myself, I find the teaching to be of very high calibre. There are a few lecturers that speak in such a monotone way that it might put you to sleep, however the content that is being covered is very interesting and there is also some fantastic lecturers about too, some of which you'll get to meet during first year!
3) There is a lot of support offered for first year students, whether this be tailored drop in sessions, which will help to break down the difficult concepts being introduced or PhD helpers that are available during all the problem classes you'll have assigned. If these aren't enough then each lecturer will also have their office hours available, so just pop by and they'll be happy to help you with whatever you're stuck on.
4) What do you mean by this question? Do you mean work or extra things that the university has to offer?
5) That really depends on how keen you are, the lecture notes that you'll be provided with for each module will be more than sufficient to help you pass the exams, however if you're interested in a particular concept and want to see the extensions from that concept then you can find a book in the library and do some extra reading, but this isn't required to pass the modules.
6) For me Nottingham was ranked as my insurance with Warwick being my firm choice, however I'm not bitter about missing the grades for Warwick because Nottingham has so much to offer me and if I went to Warwick I don't think I would have the same opportunities.
7) I applied with AACU in Maths, Further Maths, Chemistry and Biology respectively and my offer was A*AB where the A* was in Maths and the A in Further Maths.
8) There are a few, however this will vary depending on the strength of the years cohort, so don't rely on getting in with lower grades than required, however I imagine you've got a pretty high chance of getting in if you just slightly missed the offer.
9) Well since Maths is quite a universal subject, it's quite hard for modules to be unique to a particular university, just because everywhere, in the top universities, will cover the same content just in a different way. A few modules I did enjoy in first year were ACF - Analytical and Computational Foundations, CAL - Calculus and MSS - Mathematical Structures. I'm now currently enjoying my Vector Calculus module and next semester there are some modules called Complex Functions and Differential Equations and Fourier Analysis which both sound super exciting!
10) I'm currently looking into a career in Investment Banking, specifically Trading or Structuring.
I hope this answers all the questions and if you have any more then please feel free to ask.