My DD graduated from Cambridge last year and is now back there doing a PhD. She studied NatSci which has a massive cohort.
Lectures, as others have said, are subject-based so students from all colleges attend. Tutorials, or supervisions at Cambridge, are 1:1 or in the 1st year 2:1 or even 3:1 either in your own college or another one depending on numbers and the availability of the tutor/supervisor. In NatSci, DD has 7 students that she supervises: 2 x 2 and 1 x 3. They are all 1st years.
DD almost entirely self-catered for her 4 years. The gyps (kitchens) are not great, but students are ingenious and creative. In her 4th year, DD and her floor managed to cook a 5 course Christmas meal using them (they may have cheated and bought a table-top oven). In her 1st year there was a minimum catering spend of £85 per term which DD bitterly resented but that disappeared. Having said that, on Sundays they do a nice brunch at 11:30 so she & her mates would have that.
In terms of support, DD's college has been brilliant. A lad from the year above her at school had a nasty accident a term away from graduation. They put in loads of support for him and when it became clear that he was going to need some time back home, arranged everything and allowed him back 2 years later to complete his studies on a P/T basis. However, this may vary between colleges.
Some activities are college-based, music ones can be in college or university-wide. DD played in an orchestra in her 1st year which had students from all over the place. She now sings in a college choir which is not her own college. She rows for her college but does a uni-wide dance club. Yes, there are practice rooms.
I'm not sure it is more expensive than other universities. Terms are shorter and you only pay for your accommodation for term time, approx 26 weeks. Fees are the same as everywhere else. What they do offer is bursaries so if family income is below a certain level, there are good bursaries available. They also have college funds to support activities, so when DD was representing Cambridge in a dance competition in Blackpool, her college gave her the coach fare.
My advice to you is to check the course content and requirements carefully. Then get yourselves along to an open day, or, if it is doable over Easter, go and visit either city. Check the stats online about accommodation and whether you can live in for all the years. Then if you have any questions, ask away. The current students at Oxbridge thread is really friendly.