1) Actually as far as I've been able to find officially we don't know, and there's evidence both ways. For masks forged by maskmakers, we do know that there's standard forms, yet these standard forms are also social conventions. Maskmakes can and sometimes do deviate from the exact standard style, and masks of a completely different shape can be forged, as in the example of the Toa Hagah's masks. However, in my opinion past topics and answers given in S&T have far, far overestimated how often this maskmaker convention applies to the masks that people actually wear, for the simple reason that we only have confirmation that masks are forged from Kanoka in Metru Nui, and BS01 now states that Kanoka were only invented a few thousand years ago in story-present. Thus, for the vast majority of its history, Metru Nui and the wider MU all just had masks made by the machines that make new beings, and/or on Artakha, etc. In other words, prior to the invention of Kanoka, there probably were no maskmakers.
This results in the obvious conclusion that the standard shapes (of some masks) were probably chosen by the Great Beings when they invented Matoran, Toa, etc. in the early years. This is something we have usually overlooked (correct me if I'm missing something). So, the conventions of those ancient mask shapes were not chosen by mask forgers. (Though since Kanoka were invented, new mixed powers were made, thus new shapes had to be invented, and those were chosen by forgers alone.)
And then this gives us two possible answers to cases like Toa-izing.
First, if something like my old cyberclay theory is correct about the protodermis molecule, large amounts of data can be stored in its particles. So, all Kanohi particles could store a memory of the original GB-chosen standard shapes, so for those powers (which likely includes all 12 of the 2001 mask powers, including the Toa Metru's six), the transformation itself triggers those shapes. Evidence for this includes the fact that protodermis already stores data in how to run protodermic powers, masks can have imprints of "spirits" attached, etc.
Second, the "mental image" theory is correct. Evidence for this is that for the shape of the Toa themselves, Greg directly confirmed this is what determines their shape. IMO this one is more likely (not that I disagree with my cyberclay theory -- just no need for it to explain this part). Each of the six was probably aware of the standard Great and Noble shapes of the Matoran masks they had on -- and probably aware that the maskmakers who had made theirs had stylized them for Matoran.
A third possibility is that the GBs programmed a mental image of those shapes into all Matoran's minds, rather than protodermis particles (included in the standard knowledge download they get from the spawning machines, along with language, etc.). And in the case of new masks, they might learn them, or the particles might, or the machines might.
So basically, we don't know exactly which is the case (or I don't, as far as I recall -- but Greg might have answered it on the old forum).
2) The question really is why Vakama didn't know which shape went with which power (and whether he didn't; read on), since he was the one with a job like that. Nokama and Whenua also could have been knowledgeable about such things, being a teacher and an archivist. We wouldn't expect Onewa, Nuju, or Matau to know it.
Greg did give an official answer to this at one point, I believe, but I've lost track of exactly what it was. It's often discussed and there are a variety of theories about it. But I'm pretty sure the main answer is Toatapio's answer.
And Vakama might have known what the powers were, basically, if only because the names of each mask are words in the Matoran language that they all knew, which were the names of the powers. In that case, what northmarch said would be the basic answer. Knowing as "book knowledge" that "this shape goes for the power named this" isn't the same as knowing how to use that power, or knowing exactly what the nuances of it are. It appears you have to learn something like that to use masks, which is why in all other cases in the story there was something that provided that knowledge for Toa (the Nuva were formally trained, the Inika's organic masks informed them, and as Mahri the Ignika informed them).
3) Greg told us the "why", if not all of the "how", for Jaller's mask. He said that it turned back to the Great form (but chose the standard) in order to honor Lhikan for what he was in most of the time the Matoran knew him, as Toa Lhikan. This seems to be evidence for the mental image idea, that Jaller was more familiar with the standard (Tahu-style) Great form, or his particles were set to that shape.
As for the how, it appears that such a transformation can occur when a person is given a new mask, although it might only be due to its being a powered mask, or Lhikan's spirit still being attached, or something.
As far as I can tell, the 12 original Kanohi designs are the only ones common around Metru Nui ( Metru Matoran masks being shaped like great masks is artistic licence to make them more recognisable).
Common, perhaps, but we do know there were others, from Sayger's canon art (including some of the powers I got Greg to canonize), when some Matoran were shown when the five Toa Mahri were teleported back to Metru Nui at the end of 2007. Also, in the past three thousand years or thereabouts, the shapes of the new powers might have become more common there than elsewhere in the MU (though still rare overall) since Kanoka were invented there.