Well, hi there, I happen to be a student in the UK. To answer your questions:
The weather is mainly rain - as you'd expect. The westcountry (southwest - Cornwall, Devon, Somerset, Dorset etc) is warmest and wettest - and is also the main holiday destination. Snow is rare, but so is really hot weather! Scotland is the coldest, along with North England. The Southeast (which includes London, Cambridge and Oxford - just) is the hottest and dryest area of the UK, but there isn't actually that much difference.
London is by far and away the most expensive part to live in (most expensive city in Europe apparently) - rent there is double that elsewhere for a room/flat of half the size. Basically the further North or West you go, the cheaper it is.
As for travel in the UK - connections between Ireland and GB are best made by plane - companies like easyjet, go, bmibaby are the most likely to give you cheap tickets. Within GB, neither train or bus is great, but I much prefer trains - when they run. The railways are going thourgh a bit of a crisis at the moment, so trains running several hours late a pretty normal. Coach is awful (really cramped if you're 5'11"), but if you're going somewhere obscure they might be an idea. Get yourself an ISIC card (?6 -whatever that is in dollars) and then get a Young Person's Railcard (?18 - valid for a year). This gets you a 1/3 off most train tickets, and always book at least 2 weeks in advance otherwise your pocket will really feel it (for example, if I want to travel Plymouth to B'ham return (about 200 miles) and book 2 weeks in advance I pay ?10ish, but if I book the day before I pay ?100ish - big difference!).
Living all over varies so much - students sharing a student house normally pay about ?45-50 a week (except in London - about ?90/wk there). If you're renting on your own in professional acc the price rises quite dramatically.
As for studying in the UK, I've only got experience of Med Shool here (since this is my first degree), but I'm told (I don't know how accurate that is though!) that american degrees are a lot more structured than UK degrees with more timetabled teaching etc, so you might find it a little unstructured to begin with. As far as medicine is concerned, it's pretty much the most structured degree there is in the UK, but it varies between Universities.
England generally is quite an expensive place to live, especially if you want to run a car (easily the best way to get around) - petrol, insurance and tax all just keep on going up (I pay (approx!) ?180 tax/yr, ?500/yr insurance and a minimum of ?10/wk on petrol at about 78p a litre). Alcohol and Cigarettes also have a big markup on them, so buy them duty free (which you can do easily enough by crossing the France/UK border, esp if you're close to London).
Got to go do a presentation about Audit, so I'll stop there!