Glad it was useful.
Hard to say how people feel. Some people are constantly intimidated. But most people, IME, get used to it all. And even enjoy it. Because when else do you get to live cheek-by-jowl with buildings that look like that?
A friend's DD at Durham felt the same way! 
I do not think most Oxbridge students are super confident. Some may act confident better than others, but it's hard to be too full of yourself when you know everyone else is good, too. I think that's true of university in general.
Occasionally, you might meet someone in freshers' week, or at an Open Day, who seems to have it all sorted out and who might come across as if everything naturally fell into their lap and only they know how to fit in. And, those people are either the sorts of arrogant jerks you can't avoid meeting in life, or they're just 19 year olds who haven't yet learned how they come across - they're not actually any more likely to succeed than anyone else. This is true of every university I have ever heard of.
I can see crises of confidence from both sides. On the one hand, undeniably there can be a bit of a valorisation of stress at Oxbridge, which isn't great. But, there is also a lot of contact with your teachers, who do have vested interests in helping you figure out how to manage stress and how to stay the course.