Air Tahiti Nui is your "go to" airline to PPT., though HA flies on Saturdays, and I think AF may still fly there on a limited schedule as well. Others that used to fly there now merely code share with TN (I do miss the QF 747SP!)

Air Tahiti is your a airline to BOB, but you can't use any airline's miles on it. Expect to pay $400-600 per person R/t for this flight.

Frankly, Bora Bora is very expensive and offers beauty and relative isolation. You can get about as much beauty, with less expense and many more activity and lodging options at Moorea, and get there by fast ferry from Papeete in a half hour.

Yes, I've been (several times, including other islands and Rangiroa out in the Tuamotus). We really enjoy Moorea for a pleasant holiday. (For high voltage diving, lots of Pelagius including sharks, Fakarava and Rangiroa are top notch. But I've had good diving at other islands, including Moorea.)

Be aware: high demand and prices July and August (it's all a French Overseas Territory, so, lots of French visitors and tourists for the tropical benefits. Also be aware the rains begin in December and can bring tropical storms lasting days.