Answers to your questions:
1. OWBs are much more expensive in Bora Bora vs Moorea, however pricing varies from resort to resort as well as different categories of rooms. Some resorts have discount packages at different times of the year as well (ie: stay 4 nights, pay 3 and things like that). You'll have to look into specific resorts to find pricing.
2. The only way between Bora Bora and Moorea is a flight on Air Tahiti (domestic carrier, not Air Tahiti Nui). It's about $400-$500pp round trip. To get to Moorea from Tahiti (where you will land) is a $30 ferry ride. To decide whether or not you want to do both, you first need to take into account the amount of time you have and the added expense not only of the flight to BB, but the lodging, food, excursions, etc are all at a premium on BB as well (vs prices on Moorea).
3. Renting a car in Moorea may be worthwhile for a day as you can explore the island and do a little shopping in the few stores on the island. I can't really see it being worthwhile in BB. Most resorts in BB are not on the mainland, rather they are on Motus (islands) in the lagoon surrounding the main island. This is nice as you are secluded and have a wonderful beach and view of the mountainous mainland, however you are also "trapped" as most resorts charge a fee for a water taxi across to the mainland (because they want you to eat at the resort). If you want to see the interior of either Moorea or BB, I would recommend an ATV tour or a 4x4 tour as opposed to a rental car. If you just want to explore and stop & go at your own pace, a rental car would be fine.
Do a little more research online and on Tripadvisor, let us know how long you'll be there for and what your main interests are and we can make more suggestions. You said you are active, so I recommend you spend more time on Moorea as there are some nice hiking opportunities there (not many on BB from what I've heard anyways).
Have fun planning!!