JZ,
Americans actually add quite a lot to the University of St. Andrews. What makes St. Andrews great, I believe, is that it carries such a cosmopolitan atmosphere. There isn't really an 'in-crowd' and there is always a potential to creat your own niche. Some answers to your questions are written in the newly revised 'Disorientation Manual' re-edited by Carson Moss(an American from DC). It offers a lot of helpful information.
About the JYA thing. Getting into St. Andrews as a JYA is a pretty easy task, you only have to apply and beat out the rest of the applicants from your particular school. The competition individually is pretty slim and the class sizes within the University are built to sustain an added number of pupils.
On tuition: Americans stand to pay £7,900 pounds (I believe... guessing on the usual 400-600 pound increase per annum) for one year's tuition. Hall fees are extra. I don't know how much they currently are.
If you were trying to get into the University as a first year from abroad, you will have an uphill battle. The University is notoriously hard to get into from the States, despite what some people may tell you or despite some of the Americans you may meet who are actually studying here.
The entry rate is very low and it doesn't take away from any of the British entrants because the UK government has it set up so that there are a minimum number of students required to attend this fine University(providing they meet the entrance requirements laid out by the University) Only the University can accept or deny entry and they will be very sure not to do either on the basis of a quota. So you are not taking away from a British student.
Come on over and I hope you have a great time! And take heed what a couple of the previous statements were about... mainly the one about the Brit's making fun of you... it is almost always good-natured.. and try and get a few back at them!