Could you please let us know when you are going as it helps to give you more accurate advice. We rented a car but young friends of ours rented scooters. Your preference I guess but I wouldn't want to be riding a scooter in a tropical storm! Speed limit is 50 kph.
I always prebook what I can but I guess it depends on when you are going to Raro.
Tamarind House is a great restaurant. Trying to think of the other restaurant we enjoyed a meal at. Just remember that almost all their food is imported and sometimes stocks are low if weather conditions are adverse. We discovered that when we were there 2 years ago - even the restaurants were experiencing difficulties.
Most shops in Avarua (main town) close at 4:30, although the supermarkets are open later. I bought my black pearls as loose pearls at the Beachcomber Pearl Market, but lots of places sell black pearls made up. Hopefully someone else will be able to advise you about this.
Captain Tama's lagoon cruises are a lot of fun, and you have the opportunity to snorkel and swim in the lagoon with the fish.
I will have to look for my diary and the information I found when researching our trip. We had a wonderful 12 days on Rarotonga, in spite of the edge of a tropical cyclone crossing the island and causing some rather interesting weather at a time when it was supposed to be calm!

Aututaki is well worth a look, assuming of course that you like snorkelling and white sandy/coral beaches and all that goes with it. I would book in advance, then you are certain and can plan around it.
It is nearly 20 years since I went, but we didn't need a car or scooter, the round island bus was very cheap and efficient. One goes clockwise on the hour and the other anti clockwise on the half hour (from memory).
The horseriding was fun riding along the beaches.