The Toa Kaita were two distinct beings formed by the merging of the six Toa Mata. Akamai was formed from Tahu, Pohatu, and Onua, and Wairuha was formed from Lewa, Kopaka, and Gali. After their battle with the Manas, the Toa Mata were not seen to form Kaita since that time. The Toa Metru had the ability to form Toa Kaita but never did so since they lacked knowledge of the technique.
Greg always saw the Kaita as a new entity or mind formed by the merging of the three, instead of three minds controlling the same being. All beings involved in a fusion would retain memories of their time spent united like they normally would, although it would be from the perspective of the collective mind.
When Akamai and Wairuha were formed, they instantly knew each other by name, probably because there was some sort of base programming to ensure that they would not end up fighting each other when they came into existence.
Each Toa Kaita had the elemental powers of all three Toa that made it.
A Toa Kaita's mask power was always the combination of the mask powers of its constituent Toa.
All Toa had the ability to form Toa Kaita.
Any three Toa could form a Kaita, but it worked best if the three had different elements.
There was no set combination of elements a group of Toa needed to have to form a Kaita.
If Toa Kaita of different element combinations from Wairuha and Akamai existed, they would have had different identities from Wairuha and Akamai.
If a Toa team besides the Toa Mata or Toa Nuva made Kaita with the same combination of elements as Wairuha and Akamai, those Kaita would likely not be considered Wairuha and Akamai.