Not in the ask category because this is just a fun discussion topic…
What do you guys think would happen if a rahkshi of accuracy and a rahkshi of dodge of equal kraata evolution engaged each other in combat? What if two Makuta replaced said rahkshi in the situation, one using a Calix and one using a Sanok?
Dodge wins.
They can dodge, but they can still hit accuracy.
That just makes it easier to hit them
Unless it predicts the dodge’s movement
Just because dodge is impossible to physically strike doesn’t mean you can’t accurately hit a lever which dumps a bucket of molten lava on them, right?
You specified that they are of the same intelligence, and I think that victory is dependent on that. If both are stupid, then dodge wins. The smarter they get though, the more I think accuracy can find a clever way to win. For example, suppose I aimed my shot, knowing my enemy would dodge, and when they did, they slammed their head into a poll?
Dodges pole too.
What now?
I’d say this actually depends on how exactly the Dodge ability works. Since it’s described in Makuta’s Guide to the Universe as “impossible to hit physically, no matter how fast or strong the attacks” it seems to indicate that the Dodge ability doesn’t describe doing something but rather taking on a certain state - after all we know that Makuta don’t have the ability of super speed. I imagine that while active this ability kinda warps space around the Makuta/Rahkshi/Kraata which makes it seem to move really fast when in fact it’s rather the attacker’s blows that are diverted.
Accuracy on the other hand is described as “Able to hit any target on any distance independent of surroundings and state”. So if Dodge is a state, I’d actually say that Accuracy enables someone to actually hit a Dodge user. However, if you see the attack coming way ahead you would be able to normally dodge even an attack using Accuracy if it was aimed at the spot you previously were in. Because I believe that once the attack is started the attacker can’t influence it anymore.
(Makuta’s Guide of the Universe stuff translated back into English from the German version (which by the way is sometimes really bad), so if I got anything wrong there, feel free to tell me)
Hmm… I personally think it will result in a tie IMO.
I completely agree. To understand how Dodge ability works, I find it helping to look at previous evolutionary stages of it.
Stage 1: Surprisingly difficult to catch.
Stage 2: Fast enough to evade the most skilled disk-thrower on Mata Nui.
Stage 3: Quick enough to crawl circles around an enraged Husi pecking bird.
Stage 4: Able to dodge faster than a Tarakava’s strike.
Stage 5: Skilled enough to dodge even Pohatu Nuva’s speed.
Stage 6: Impossible to physically strike, no matter how swiftly or powerfully.
While it’s not exactly super speed per se, descriptions for Dodge seem to suggest that user of this ability will be able to move really fast, to speed that rival even Pohatu Nuva’s in later stages, even if just for evading attacks.
Meanwhile, Accuracy to me seem to describe ability of attacking a specified “target” with greater and greater precision, across longer and longer distances as it evolve. This will result in something like a “sniper” skill.
Stage 1: Instinctively seeks out the most vulnerable part of a target.
Stage 2: Able to strike and infect a nearby target perfectly nine times out of ten.
Stage 3: Has the ability to strike a close target with unerring accuracy.
Stage 4: Can strike even a remote target with near-perfect accuracy.
Stage 5: Able to leap and strike with perfect precision, no matter the circumstances.
Stage 6: Can strike the smallest target at a great distance or in any environment or condition.
So I imagine a fight between these two Rahkshi will turn out in a stalemate, with each one won’t be able to really attack each other. Assuming that these Rahkshi abilites are ingrained as their permanent traits, Accuracy Rahkshi will be able to perfectly locked on its target, and fire a blast accurately to that location regardless of the wind interference or difficult terrains. However, Dodge Rahkshi will instinctively move out of the way in a speed that faster than fired projectile itself, thus moving the “target” location to elsewhere, which Accuracy Rahkshi will then precisely attack at, and so on.
While at first it might seem like Dodge Rahkshi will come out on top, it must be constantly avoiding every attacks, which are all perfectly aimed due to its opponent’s ability, so it won’t really have any time to counterattack. Thus this conflict would result in a draw. 
Battle between Calix and Sanok wearers is even more inconclusive, as both Kanohi powers are not absolute.
Calix’s power is described in BS01 as:
It allows its user to perform at the absolute peak of their natural physical abilities (such as excecuting seemingly impossible leaps, dodges, flips, etc.) so that they move and react better than almost any unenhanced member of their species.
While Sanok’s is descibed as:
It allows its user to turn virtually any inanimate object into a projectile weapon and hit almost any target they aim for.
As you can see, these Kanohi powers aren’t as extreme as above Rahkshi abilities. Calix’s power is bound by wearer’s physique, and Sanok wearer won’t hit every target. So this fight seem to depend a lot on luck and circumstances to win.
However, if wearers of both Kanohi are Makuta with equal skill at the start, I think the one with Calix will win. As said before, Calix will bring out “absolute peak of their natural physical abilities”, which in this case include Dodge ability among other things. So at least Calix-wearing Makuta will be able to stay clear of everything another Makuta throws at him, both with or without the help of Sanok. And with Calix perfecting his other offensive abilities, he should be able to gain the upper-hand and defeat Sanok-wearing Makuta with ease. 
Well, that just saved me about an hour of typing.
It can fire while dodging, it can just launch a flurry of blind fire while dodging and eventually hit the other.
Well, that’s possible. But as I imagined it, Accuracy Rahkshi would start attacking as soon as the target gets in its firing range, which should be very faraway according to its ability. So blind counterattack would be almost impossible at that distance, or any distance for that matter because Accuracy Rahkshi would intrinsically have greater chance of target hit than the opponent at any given distance.
Even if Dodge Rahkshi managed to get near enough to attack effectively, its instinctive ability should repel it right back, because within shorter distance Accuracy Rahkshi’s attack would be even more precise. Thus the closer Dodge Rahkshi gets, the more likely it is to be hit. So I think for a Rahkshi that its main ability is to evade attacks, its instinct should try to minimize probability of being hit, by keeping some distance with the opponent with such power. 
On second thought, I’m not even sure that these Rahkshi would be able to fire energy blasts, because most Rahkshi we’ve seen so far have attacking abilities, so they can fired out their power, let it be explosive energy, fear, or heat vision. Some of them don’t even have long-ranged attacks, like Lerahk or Vorahk. So Rahkshi with ability like Dodge shouldn’t be able to fire energy blasts at all. What’s it gonna shoot out? Dodge energy? 
That’s actually a good point, although… what is Accuracy shooting then? Accuracy energy?
BS01 seems to not say anything on that matter, but I always assumed that all Rahkshi are capable of firing some kind of default energy beam thing. In the Mask of Light movie there is that scene where three Rahkshi hold their staffs together and fire some kind of concentrated energy beam at the Toa Nuva. This might indicate something like that.
I’d say this “power” would not come from the Kraata/Rahkshi but rather from the staff the Rahkshi is carrying, though.
Those three are Panrahk, Guurahk, and Lerahk. Which is weird because BS01 specifically says that Lerahk need to physically touch its targets to poison them.
Lerahk use their Staffs of Poison to poison anything, be it plants, Rahi, soil, or any foe it might choose. They are immune to their own poison. They cannot use their staffs at long range, however; they must actually touch their target.
This might actually support your point that all Rahkshi might be able to fire some kind of neutral concussive blast, or it could be that they just take artistic liberty in changing things for the movie, because in the MoL book describes that scene as only Panrahk firing the blast which made more sense.
The Fragmenter-Rahkshi hissed, unleashing an arc of dark energy from its staff. Tahu lifted his shield, enveloping all of the Toa and Matoran in a protective force field. He staggered backward as the Rahkshi’s bolt hit, but recovered quickly.
But then again, there are Rahkshi that don’t shoot anything out of their staffs at all, like Vorahk that just absorb opponent’s power through the staff, or Heat Vision Rahkshi that requires its staff the access its ability but not actually channel it through the staff.
I know it’s late now, but there actually is a concrete answer to your first question: