These are great questions. They are a good part of the reason Oxbridge is sometimes regarded as a closed shop IMO
The explicit ones to do with entry requirements and, to a large extent, admissions procedures, are answered on University and College websites, and I will come back to some of them. But I appreciate that it can be very daunting to be piecing all of this together for yourself, in a vacuum if your school and your friends aren’t interested. Also, some of the websites use insider language that isn’t the most helpful.
Caius is making a real push now, not just a formal one, and the stuff they have on SM at the handle I mentioned upthread is very user friendly. Someone there told me about it.
You can only apply to Oxford or Cambridge and they have a common early October deadline. Most subjects do require an additional exam, either in the autumn or with A levels. It’s all explained in the entry requirements. Each exam has its own website and these are pretty good. Many have bursaries for those in need. STEP is the hardest I know of, but I am in STEM so have limited knowledge.
At both unis you apply to a College (or say you don’t care). At Oxford applicants to a degree programme across all Colleges receive the same offer. At Cambridge it may vary, but not hugely. The additional exam tends to be a university wide requirement.
Rule of thumb, the older colleges are grander and richer.
I think ‘gowns’ prob meant academic gowns.
Both unis have good reputations for honouring protected characteristics. Some Colleges both places are known as being particularly good for mature students, particularly progressive, etc.
As a former admissions tutor I know that different unis pick up on different contextual flags. I am not sure what if any contextual offers Oxbridge make. I do know people both places who are very concerned to attract more top students from all schools.