The politics department on the whole is excellent - I was really impressed with the lectures and the content of the different modules, but I have to admit that there were some aspects I wasn't too impressed by. I applied to Sheffield because of the reputation that the politics department had, and so far it has lived up to that reputation, for me anyway.
In lectures, you basically just sit with every other student doing that module (those that aren't too hungover anyway!) and are broadly introduced to different topics and their key points by the lecturer. You then go away and do a lot of reading on that topic (usually from academic journals/essays) and discuss the topic and your reading in a seminar. Seminars are groups of about 10-15 people who simply spend about 50 mins talking about the topic, while having your tutor direct the discussion - you're not really taught anything, per se, but are encouraged to discuss what you think of that particular topic with other students.
Sheffield is a fantastic city. I come from London (so you can't quite get bigger than that in the UK!) and I absolutely love Sheffield. There's plenty to do during the day if you're bored, lots and lots of shops and the nightlife is really really good (one of the reasons I applied to Sheffield to be honest...). If being in a city with lots to do is one of the main factors you're thinking about when applying to uni (as it was for me), then don't worry, Sheffield fits that criteria!
Economics was the subject I found the most difficult as well, so you're not alone, don't worry! My advice would be get a really good revision guide (if you haven't got one already) and just read up on the different topics you do in the evening after you've done them at school. I didn't do that at AS, but did do it at A2, and it really, really helped. I tended not to understand in class, so just going over it again more simply helped a great deal.
Sorry for the really long message, but I hope this helped! If you've got anymore questions, just fire away
and good luck with your A levels and uni application!