As I understand it, most American students take the SAT exam during the second half of Year 12 or the first term of Year 13. That's probably the prime time to take it because most of what they test you on the SAT is being reviewed at high school at the same time. The SAT exam has changed over the years. I highly recommend buying the Princeton Review "Cracking the SAT." They really break it down for you and make it seem very easy. You have to sign up on the College Board website to register for the SAT.
Since you have time, you might want to consider taking the SAT IIs as well, since your GCSEs were a while ago and may not reflect your abilities now. The SAT IIs are subject tests. You take a one hour test in a subject. They are not a requirement but are good for strengthening one's application, and also for showing width and breadth in skills and knowledge. I took the SAT IIs in Mathematics I and Literature, but there are also tests in different languages, sciences, and humanities. There are Princeton Review books for these also. You can take up to three SAT IIs on one test date, but you cannot take the SAT and the SAT IIs on the same day.
I applied later than I should have - the deadline is January 15 and I sent in my app a few days before. However, some American colleges have a system called "Early Decision" in which the student applies by an earlier deadline, usually in November or December. For each college it varies, but I believe Early Decision is for students who REALLY want to go to that university. If you get accepted through Early Decision, then you have to reject all other offers from other universities and go there. I'm not entirely sure if it's like that for Chapman University though, you might have to check that. I know that film students have to apply by Nov 15th but I doubt that it's a binding agreement.
If you apply by regular decision, I would suggest starting your application at least two months before the deadline. The application would take about a month to complete depending on how hard you work, how busy you are, how many essays and references you need, etc. Try not to send it in a few days before the deadline. Common App needs a few days to process the application fee before it sends off your application, so if you pay on the deadline it means your application will be received a few days AFTER the deadline. Glad I caught that at the last minute, lol...
As for your chances, I'm afraid I don't know. I don't even know if I got in myself yet! But don't worry, if you work hard on your SATs, your personal essays, and spend the next year getting some great extra curriculars (they LOVE leadership activities btw) then I'm sure you will have no problem getting in. You have plenty of time!