You've had quite a few answers to this already but here goes...
1. A binder for each subject is very useful to keep your work organised and neat. If you can get into the practice of sorting them into bigger binders at home, this will be great for revision. I used binders religiously at AS and then fell out of the habit once I got to A2, and ended up losing a ton of my classnotes which was really frustrating. I'd recommend getting your own lined paper too, tightened sixth form budgets mean that they prefer you to have your own supplies.
2. No way! It's definitely a good thing. Ensuring that you're all ready for the new term to start in September will mean that you'll have one less thing to worry about on top of starting a new sixth form. A glance at the specifications of the subjects you'll be studying, particularly those that you haven't encountered prior to A Level e.g. Law and Psychology, can be useful too so that you can begin to familiarise yourself with them, and complete any summer reading or summer work you've been assigned as it'll set a good first impression. Yes, that sounds like something a teacher's pet would say, but honestly, setting a good first impression and getting along well with your A Level teachers will serve you very well.
3. I presume you're not Catholic then? Don't worry about it, there's probably a lot of students who aren't. Be respectful of the religion but don't let it infringe or restrict your experience as a student at that sixth form.
4. I'd recommend the brands previously mentioned, they're very durable and will protect your books well. Backpacks, in my opinion, are an absolute must for sixth form, particularly if you've got heavy books and binders to carry around. Some of my friends started out with canvas bags for the first few weeks of sixth form and ended up with really painful shoulders. Nobody's really too bothered about how your backpack looks once you get to sixth form so definitely favour functionality over aesthetics!
5. Judging by your response to Spongebob0303, I'd say go with China, especially as you've already been to New York once before. A ton of people have been to New York, China sounds much more interesting because it's not one of the top tourist destinations for British people. I presume you're volunteering at the children's orphanage? I personally find that a trip that gives something back to the community always feels much more rewarding, so I'd go with China. You'll be able to learn a lot about Chinese culture and in terms of educational links and opportunities, it'll tie in very nicely with subjects like Geography and Business. New York would, too, but I feel like you'd gain a lot more from a trip to China. It's up to you though!
6. 'I don't know if it was the teacher's voice', haha. On a serious note, have a read through the specifications for both subject and see which you find most interesting. I've heard that Sociology is easier than Psychology, and I also think it'll go better with your other subjects, but I don't know about your abilities as a student and which you'll be best suited to. Whatever subject you do decide to pick, most sixth forms are pretty lenient in allowing students to drop/change subjects within the first few weeks, so don't worry that you'll be stuck doing a subject you don't enjoy!