I just finished my first semester at IAU as well, and here is what i suggest....
1. What is the situation regarding purchasing books?
Order your books before you come to the island, i use amazon.com and bring my books with me, however, you can order your books through the school website and have them shipped directly to the school. Keep in mind though that sites like amazon tend to save you money.
2. In a related questions, my sister is in medical school and suggests that I purchase Gray's Anatomy. What do you suggest?
Not sure as well
3. How many days prior to the start of classes should I arrive on the island?
I arrived close to a week before classes started, and that gave me time to find my apartment and become familiar with the island life and gave me time to settle in. It is a personal choice, some people can come 2-3 days before and still settle in just fine.
4. Are there any supermarkets or clothing/department stores located a reasonable distance (less than 10 miles) from the school?
Yes, do not worry about that. There are two grocery stores near school, one is right near the campus. Clothing stores are there, however may not be exactly what you are used to back home. Not everything is available easily. So bring all clothing items you find important.
5. Do you suggest on-campus or off-campus housing, why or why not?
I suggest renting an off-campus apartment. Administration does a good job on setting up students. I have not heard a lot of good things about the dorms available. I live alone in an apartment and i am very happy with that. Also there is no real "on-campus" housing, the dorms are not within walking distance of the school.
6. If off-campus, will I have time to arrange housing if I arrive only on Jan. 5th?
Yes i think if you give the admin. a good enough idea of what you are really looking for then they can usually have something for you to look at the day you arrive.
7. What is the school uniform?
No uniform, just as a medical student you should dress appropriately. 
8. Finally, are there any items that you feel that I should bring, other than the given necessities?
Anything that you know you have to have bring with you because you cant be sure that you will find it on the island. Bring mosquito repellant!! If you have any doubts about any specific items dont hesitate to ask, we are here to help you!! GOODLUCK with everything and i look forward to meeting you.