Trying to answer a few of your questions as well as give you my perspectives.
North Fakarava has 3 main dive sites: the Garuae Pass, which is the main attraction and which is dived only with the incoming current; and the two sloping wall dives on the outside (the ocean side) on each side of the mouth of the pass, which are usually dived when the current is outgoing.
When diving Garuae Pass with the incoming current, most operators start in the blue, drift and stop at the mouth of the pass, maybe drift a bit to make another intermediate stop, and then drift with the current until they arrive at Ali-Baba. I would describe Ali-Baba as a valley or depression inside the Garuae Pass. It is usually full of life, with big schools of fish, sharks, and Napoleon Wrasses. When it is good, you could easily spend a whole dive there. That is why some dive operators offer Ali-Baba as a separate divesite in of itself.
I am not counting lagoon dives as options: they are not what you fly all the way there to dive. I did it once when the weather was really, really bad.
As has been mentioned already, you can dive the Tumakohua or South Pass of Fakarava while staying in the North but only if they have enough people (minimum 4, I think) to make a run to the South. Would I do it? Absolutely!!! The pass here is much narrower so the sharks tend to be less spread out, altho there are times when I have seen densely packed schools of Grey Reefs in the North as well. But what I often see in the South Pass but seldom see in the North are Silvertips and Oceanic Black Tips mixed in with the Grey Reefs. On the other hand, I have seen Great Hammers in the North Pass but yet in the South.
Lastly, some operators offer trips to Toau, which is the next atoll north of Fakarava, but that is an ocean crossing so the water conditions must be favorable. And it also requires a minimum number of divers.
Kaina Plongée, which is the operator I've done all my diving with in the North dating back to when it was Fakarava Diving Center, does offer trips to Toau. I don't know about the others. Would I do it? Only as a change of scenery: there are two passes there not too far from each other. But, in my opinion, you are not going to see anything different - same sharks, same fish, maybe a manta.
That pretty much covers the divesite options that you will be offered when diving with a North Fakarava operator.
In Rangiroa, not counting lagoon dives, there are basically three divesites in all: Tiputa Pass, the sloping wall on the outside and to the right as the boat comes out the pass, and Avatoru Pass. I've done only done Avatoru twice in 7 trips.
I've dived Tiputa Pass both with the incoming and the outgoing current, so two different ways of diving the pass. But incoming is best because the viz and the marine life are so much better.
A variation on the third divesite that at least Raie Manta Club - the operator I use - does is to drop in the blue in an area where fishermen used to dump the remains of the fish they caught. this is mostly to see sharks. The dive then continues on the sloping wall.
And that pretty much covers the divesite options you will be offered when diving in Rangiroa.
I trust that this addresses your concern about being able to dive the best spot. It's not like there are that many divesites to choose from. To most, the best spot is diving the pass with the incoming current. If the conditions are normal, you usually get to dive it once in a day, and on a rare occasion twice, if they time it such that the second dive is done while the current is still coming in.
It doesn't mean that the outside wall dives are bad. My best dolphin encounters of the tummy rub variety in Rangiroa have mostly been out there rather than in the pass.
June is a busy month for a couple of reasons: in South Fakarava, the annual Marbled Grouper spawning occurs on the full moon of either June or July and sometimes both. That is a spectacle in of itself before you add the increased number of sharks that show up to feast. In Rangiroa, it is Grey Reef mating season.
I have not stayed in any of the North Fakarava pensions that you mentioned. In the past I have stayed at Havaiki, Pension Tokerau, and Pension Kori-Kori. All were pretty good, but Havaiki stands out as the best.
Not trying to be sarcastic but Fakarava North is any place that isn't South, because there is really nothing in between.
Likewise, I have not stayed at any of the Rangiroa lodgings that you mentioned. I've heard good things about Bounty from a friend who stayed there. The places I have stayed at are Raira Lagon and Teina et Marie. Raira Lagon is nice. Teina et Marie, as well as it sister pension next door, Pension Glorine, are OK - better suited for the frugal-minded (like me): a bit on the rustic side. But staying there means that I am 150 ft away from my dive shop, and about 3 minutes from Chez Lily (see below). Teina et Marie is one of those that also communicates thru FB.
Most pensions offer a half-board meal option, which is breakfast and dinner. Lunch is on your own. In Rangiroa, I usually have lunch at Chez Lily, which is next to the dock. And when I do not feel like a heavy lunch, there is another "Snack" up the road heading west, about 12-15 minutes from the dock, that serves decent subs. A "Snack" could be described as a small cafe. There are also a couple of foodstores 5 minutes away from the dock.
I've encountered mosquitoes every time I've gone - whether January, February, April, June or October. Most places have mosquito nets or screened windows. Having AC or a good breeze helps.
In North Fakarava, there is just the one main village called Rotoava but there are a few small "Snacks" furtehr away from the village center. For example, there are two that are close to Pension Kori-Kori, which is also near Pension Veke-Veke.
In Rangiroa, you could say that the village of Tiputa is split in two by the Pass, with the west side being where the dock is, and where most of the hotels and pensions are, and the east side being where thevillage schools, churches, etc. are. And then there is the village of Avatoru further west, past the airport.
Currents vary. Sometimes they can be mask-ripping currents. Sometimes they are mild. And sometimes there isn't any incoming current if the lagoon is overflowing with water.
