You apply through the UK version of the common app. It’s called UCAS. You can list 5 universities or courses only. The same app goes to all unis. Each course will have entry requirements which are listed on their websites. You should not apply unless you are confident of having what they ask for. If you are taking classes as a senior, you will get a conditional offer, which means acceptance is conditional on making the grades they ask for. Oxford will require the HAT in addition - there are practice papers online. Deadline is October of senior year for Oxbridge and January for everywhere else.
No, you cannot apply to both Oxford and Cambridge
They will list out their entry requirements per course. e.g. 3 As at A Level including History. In US terms that would be 3 APs with 5s including history (I’d advise against US history for this: do Euro). After these entry requirements, UK universities are looking for students who are passionate about their subjects and who read widely around the topics. For Oxford, they will expect your Letter of Rec to say that your daughter is one of the best history students they have ever taught. Applications are reviewed by teaching faculty not admissions officers: they are deciding who they want to teach.
Yes, you must submit all tests
Not really interested unless directly related to the subject you’re studying. But it is NOT the same as at US schools. No need to ratchet up a ton of ECs. They really don’t care: they just want the brightest students who are passionate about history. Remember: the app is read by teaching faculty.
Study, read widely, learn to write well and get 5s on the APs! For Oxford, practice for the History Admissions test (HAT). Understand what is expected for the Personal Statement (NOT the same as an American application essay!) and Letter of Rec.
Now answers to questions you didn’t ask, but would be good to know:-
ALL the info you need is on the uni websites, including entry requirements for US students.
Encourage your daughter to read through the detailed info on which classes she will be taking. There is very little wriggle room in an English uni course. Make sure she is happy with the classes, as courses can differ across unis.
Teaching/ contact hours will be minimal, and there is an expectation that most work is self study, done independently. There will be a LOT of reading and essay writing. Your D will be expected to read a variety of sources for each essay/tutorial - there is no one set textbook per class. At Oxford, she would have tutorials with 1-2 other students where essays are discussed and critiqued in the group.
Grades are based largely on a couple of submitted essays and end of term exams; there is minimal continuous assessment. Does your D thrive in a high stakes exam situation?
There is almost zero hand holding of students in the UK and a large degree of self advocacy and independence is needed. Especially in London. Your daughter will be treated like an adult.
Drinking age is 18 and lots of socializing, even official faculty events, will involve alcohol.
There is no financial aid available
Oxford terms (semesters) are 8 weeks. It is intense. Then there is catching up on all the work you didn’t do during the vacation!