In my subject (I'm a tutor in one of the big arts subjects -- name changed because I don't want this information to seem specific) we would never waste another college's time during a very hectic process by sending a candidate over whom we'd already decided to place. Undergraduate interviews aren't something we use to 'brag' about our own college, and I find that notion odd.
The process in my subject goes like this: we make up a list of candidates to interview and at the end of the first day we send home the people we've decided to take (i.e. people who were so impressive we want to make an offer without seeing the rest of the pool) and ones who were so weak that we can't imagine they have any chance of a place at Oxford. (If someone lives so far away that they need to stay for logistical reasons that's obviously fine.) Everyone else stays overnight and gets a second and possibly third interview over the next two or three days at another college. Getting a second interview implies a candidate is still very much in the running both at the original college and at Oxford generally, but also that they haven't impressed us so much that we've snagged them. (The only exception would be for people at the end of the list, who might have a second interview before their first, to make sure we don't give them less of an opportunity to get in.)
I think candidates who do stay up often have a pretty good time, and are noticeably more relaxed in later interviews. We do not monitor what they do outside the interview context at all -- there is no mechanism for us to capture feedback, and we aren't interested. (Outside burning down the college buildings, stealing the candlesticks...!)
It'a a good idea for candidates to keep checking the list posted in the college they applied to to tell them about subsequent interviews -- it is always a bit depressing when people miss them or are late/ unable to find the second college etc. Everything happens fast and chaotically, so they need to be organised. Get a map of Oxford, work out walking distances etc.
On a more personal note, now I'm thinking about interviews. Please, please tell your DSs and DDs not to pre-prepare a spiel about their interest in the subject / Oxford which they then mechanically start on (sometimes from nerves) despite the interviewer going in a different direction. It wastes a lot of time and it costs potentially strong candidates places, because we aren't able to engage them properly with the question in hand, which is intended to be something that no one has thought about before! (Of course, one or two people always have but we are trying as hard as possible to be fair to candidates from a very wide range of backgrounds). And my other bugbear: if the interviewer corrects you on a point of fact, go with it they're intending to be helpful, and to promote further discussion. There is nothing good about feistily defending an error (e.g. a misunderstanding of a technical term or rare word in a document), though I think candidates sometimes do this in a misguided attempt to show they can 'stick to their guns'.