Hey there, it sounds like you have a lovely trip planned! :)
Don’t be afraid of customs, you’ll be absolutely fine. It is set up to be intimidating, or at least feel very serious (for obvious reasons – airports are one of the very few places in the UK where our police are armed). Aside from the obvious things (i.e., being jocular about terrorism/bombs etc.), you won’t have any trouble if you just follow the instructions and make sure you aren’t carrying anything unsuitable. In all honesty, I actually think the UK’s airports are far less intimidating than those in many countries in Europe. It depends on the size (bigger ones tend to seem a lot more formal with regards to security), but I really wouldn’t worry about it.
I live just over an hour away from Bristol in the South West, and it’s a really lovely part of the country. Unfortunately I don’t know Bristol terribly well (having only really passed through it on my way to other places), but I gather there’s lots of stuff in that area that’s worth visiting – I’m sure a local could help out more! I haven’t been, but I gather Bath is a lovely town worth exploring too. I’m not sure whether you’ll have access to a car, but if the weather is fine and you’ll be here for a month in summer, I’d really recommend exploring into Devon (where I live) and Cornwall. They are really beautiful places, and although certain parts can get very toursity during the summer months, it’s not hard to avoid the crowds! I don’t know if you’re a fan of the outdoors, but I would recommend exploring both inland (e.g., Exmoor, Dartmoor etc), as well as coastal places – the south Devon coastline is very beautiful and has lots of sleepy old estuary towns (Dartmouth is lovely) and places that have a load of beautiful Regency buildings that have a sort of faded beauty, whereas the north coast of Devon and Cornwall tends to be much more dramatic, I suppose because it’s beaten by the Atlantic! I honestly think that you could go almost anywhere in this area and not go wrong – I’ve not lived here long but I absolutely love it, so beautiful.
With regards to culture changes and customs, I can’t really think of any obvious ones that would crop up for you (I’m assuming you are somewhere in North America!). I think you’ll find people very friendly and welcoming, the South West is a really great part of the country. With many businesses and people in this part of the UK reliant on tourism as part of their livelihoods, people are very welcoming and happy to see people from other countries. I personally love meeting Americans and Canadians, and people from all over the world – it’s so interesting to meet people from other cultures, and folks will love your accent!
With regards to the ID situation for clubs and bars, I can understand why you aren’t keen on taking your passport with you. Some places will accept photocopies of passports, but obviously these are prone to being forged by keen underage kids and so it’s not a foolproof solution! I’m not sure what your US ID is like, but basically, most places will accept a form of ID so long as it contains a photograph of you, your name, and your date of birth. For many people in the UK this is their photocard driving license, but unless somewhere has particularly objectionable bouncers, they should accept forms of ID from other countries too! If you look under 25 you can expect to be ID-ed, particularly if you’re going out on a Friday or Saturday. I’ve only just started not getting ID-ed so much (I’m 24), but still find myself being asked to show proof of age when I’m buying a bottle of wine along with a load of other (sensible and boring) groceries at the supermarket! Don’t be embarrassed about it, it happens all the time.
Regarding currency change, a number of stores in the UK never charge commission, so when I want to exchange money, I usually head to one of those (usually I go to Marks and Spencer (a well-known department store in the UK), or the Post Office). I don’t know what exchange rates are like, but I like not paying an extra commission fee!
Phew, that turned out longer than I had planned, but I hope you find some of this helpful, and I hope you have a great time on your trip! :)