ABOUT THE COURSE
Computer Science is a very mathematical degree at Oxford. Expect very little practical programming experience - there's no typical imperative programming until January and even that only lasts for a couple of months. However, this is actually a strength of the degree because you can learn to program whenever, but here you'll learn the reasoning skills to construct correct and efficient programs. This mathematical aspect is still the case on the single-honours degree (not joint with maths) so keep that in mind when deciding the between the two!
It's difficult, with a lot of long problem sheets. However it is fun to learn about new things way more thoroughly than you've ever done before, and it makes you a much better problem solver overall. There's a lot less coding than I expected though - I would encourage continuing to code as you'll need it in second year
THE APPLICATION PROCESS
Computer science interviews can be really varied. Some tutors and colleges prefer much more mathematical questions, others prefer brain-teaser style ones that test your logical thinking. The best thing to do is practice on both, and practice being able to talk through your thought process as you go - chances are you'll take a wrong turn along the way to the solution, but by talking through it, your interviewer can catch you sooner!
Treat it like a conversation! Take it as a chance for you to talk about intellectually stimulating maths/logic problems with intelligent people, rather than an assessment. You're not expected to be able to solve everything without help - just make sure you speak out anything you're thinking, any ideas even if you know they don't work, and as long as you've clearly thought about the problem feel free to ask the tutors for some help in progressing with the question.