We just returned from a 19-night trip to the Society Islands. We visted Tahiti (6 nights), Moorea (7 nights), and Bora Bora (6 nights). I haven't been to Fiji or the other islands you mentioned in the OP, but I can answer a few of your questions with regards to these islands.
1. When to go? Definitely avoid going in rainy season. We have friends who went for two weeks in Dec-Jan and they said it rained too much for it to be very enjoyable. That said, the dry season is high season so prices will be higher for accommodations, etc and things will start getting booked up. We started booking in late July for our Sept-Oct trip, and there was very little availabiltiy in early Sept, especially on Moorea. We weren't able to find a solid 6 nights' accomodation on that island, so we ended splitting those 7 nights between 3 different places.
2. Which islands? This was our first trip, so we just stuck with Tahiti, Moorea, and Bora Bora. Tahiti was worth a few days IMO -- we rented a car and enjoyed driving around. But I know others on various travel forums find it the least interesting of the Society islands. You'll probably need to spend one or two nights here just due to flight schedules in and out. Bora Bora was alright, but we much preferred Moorea. There was much more to see and do, a wider variety of accommodations, and the snorkeling was great. Other islands that were recommended to us were Taha'a and Huahine, but we wanted to focus on the main islands since it was our first trip.
3. Activities? You already know about snorkeling and hiking. On Moorea we took a guided snorkel tour early on and they showed us some of the best spots (particularly just off Temae beach near the Sofitel). The guided tour included sea scooters which was really fun, and they took us by boat from the east side of the island to the south side, so we got to see quite a bit. We would have liked to rent our own boat and snorkel on our own -- we had actually booked a couple of days' rental for our Bora Bora stay but then weather caused the company to cancel. We were also on Moorea during humpback whale breeding season, and went on a whale tour with a marine biologist which was really informative and we did see whales and hear the male sing underwater.
4a. Lodging recommendations? Most of the travel forum posts we've seen have been about the Over-Water Bungalows (OWB). But we bucked the trend and just booked homes and apartments via Airbnb or Booking. We were still able to get waterfront property (snorkel from the backyard), but for a much better rate. Some of the big resorts do offer day passes. For example, we were able to spend the day at the St. Regis Bora Bora and it was wonderful and included lunch, use of the pool, and non-motorized water sports, like kayaks. So that was a way we could get the best of both worlds. Be aware that in high season at full occupancy, the resorts may not offer day passes. I had to call around -- the Conrad and the Four Seasons both gave me a polite but definitive "non". [emoji23]
4b. Dining recommendations? On all of the islands we visited we saw many "roulottes" (food trucks). Unlike food trucks in America, these usually are permanently located and have seating areas. Look for them at the Vaitape and Puna'auia docks on Tahiti, and in various locations around Moorea. They are an economical alternative to resort dining, and the food was pretty good. We also had one of the best meals of our trip at Holy Steak on Moorea (filet with foie gras). Great views, and they have happy hour drink specials too. Drinks at the resorts can be very expensive (about $18-20 for fancy cocktails).
5. Getting around? We rented a car on each island. We usually self-drive because we like having the freedom to go where we like, and leave when we want. However, you could probably just rent a car for a few days of your stay on each island, just to explore (it takes about an hour to drive all the way around Moorea, and a little less than an hour to drive around Bora Bora). Most cars are stick-shift and outside of Tahiti, the roads are typically just one lane each way so driving is easy. Tahiti does have a freeway with many roundabouts -- it's a little bigger and more hectic, but we managed well with Google maps. If you don't rent a car on Tahiti, and decide to take the ferry to Moorea, there is an Avis right at the ferry dock there.
We did keep a blog of our trip, feel free to PM me for a link or if you have any questions I can answer while our trip is fresh in my mind. We also went to the South & North islands of New Zealand in early 2020 -- those posts are on our blog too.
Sorry for writing a book!
Have fun planning your trip; it sounds wonderful!