I will give you credit for being very descriptive and very vague at the same time. Kudos, and I genuinely mean that. It shows you are responsible enough about your confidentiality but wise enough to know what’s relevant enough to be disclosed in a public website. Well done.
I am assuming your grades are very good and that you (PROBABLY) took the SSAT or ISEE, unless PEA is TO this year? Write good essays and have strong LoRs, but most of all show enthusiasm for Exeter and that you REALLY want to go there. That will go a long way.
Put all that together, you probably have a good shot. Of course, as you go up in grades, there are fewer spots, but you sound like an applicant with a great future.
Best of luck in achieving this and your dreams!