January 15th(?) is the UCAS deadline, but you could find out you have an offer way before or after then - it really depends on your application. In the majority of cases, the earlier you send it off, the earlier you'll hear back
(NB: you definitely won't be penalised if you submit it later, though, as long as it's before the deadline in January. UCAS has strict laws about equal consideration of applications as long as they're all submitted before the deadline. You don't need to rush your application if you're struggling with your school/college/sixth form) but not always. All unis have a specific deadline they have to adhere to with responding to offers, so you won't be forced to wait too long.
If you miss your offer on Results Day and they won't take you, then you'll either end up at your insurance offer or in Clearing. If that's the case, then your accommodation offer will be cancelled, and you'll have to reapply at your new university. You'll also need to adjust your Student Finance application -- it'll be the same application, but you'll just need to tell them you're going to [x] uni instead of [y] uni - since they'll be sending your tuition fees to your uni for you. All of this happens in Y13 - I imagine to stop the post-Results stress and rush on resources, especially considering there's only a few weeks in between getting results and going to uni.
Most of what I mentioned is on campus, yes! Medicine, the club, is near the bottom of the campus, close to Tuke/Williamson/Butler/Gowar/Wedderburn halls, and the Student Union is dead centre on the campus. The EWD (Emily Wilding Davison) library contains the Union Shop and is closer to the top of campus, as it faces the huge Founders Building (the huge brick photogenic Victorian chateau, you know the one) - and Crosslands, the chill bar, is inside Founders. There are also some other cafes on campus - the Boilerhouse (hipstery) is close to the Student Union, Cafe on the Square (Starbucks) is in the library, and Imagine (bubble tea and Starbucks) is close to Medicine near the bottom of campus.
Our campus is a pretty fair size - it's not huge, and you can walk from the top to the bottom in about 15-20 minutes (less with shortcuts) - but it's very green, very natural, and nicely self-contained, so you don't have to leave to grab things if you don't want to. It's absolutely gorgeous, especially in the snow and in the spring with the daffodils.
I think looking up some pictures of RHUL's campus would be a good idea! Don't make any decisions until after your Open Day --you'll be able to look around and figure out if this is the place for you. Sometimes places look great on paper and terrible in person (for me when I applied, that was Kent
), or vice versa - it's a very personal decision, and I think as long as you go into each opportunity with an open mind, you'll know if it's right for you.