To summarize, most questions fundamentally come from these 6 words. But, are there more unknown or unthought conditions that could allow us to ask (and thus eventually be able to answer) more about ourselves and our universe?
Example: if ‘when’ didn’t exist, would we think as much about time as a concept, or would it even be a concept at all?
The English words for use in questions don't have much to do with the range of things we ask. This set is conveniently mnemonic, but it is not otherwise special.
It could be smaller: We know, for instance that spacetime is unitary -- 'when' might just as well be 'where'. And even before physics got that far, it has been so in other languages, which have an 'at' that applies to both space and time and basically ask 'at which'.
It drops whole categories of questions, for which we then invent odd idioms. "How many/much/long?" translating 'Quando?' has nothing to do with any other meaning of "How?".
It also already conflates important distinctions: We know that 'Why?' means at least four very different things, as it can capture any of the types of causes pointed out by Aristotle: "Through what process?", "Unto what end?", "On account of what prior circumstances?", and "Because of what concurrent facts?".
And its divisions are not clear. For three of those meanings of 'Why?', we also use "How?" making a total hash out of propositions like "Science prefers 'how?' questions to 'why?'questions." (There is content to the assertion, but it is not logically connected to questions that can really be asked with those pronouns, since those overlap broadly.)
This is a case where we use ambiguity and incompleteness to our advantage. We know that questions are seldom complete and need to be analyzed. The poor tools generally do not get in the way of far more complex meanings than one would expect.
You can tell by the forms in most of Latin, that it started out with one basic root for most indefinite constructions: 'quo'. With a few major exceptions like 'ubi' everything is timeworn abbreviation of some general sentence construction with a form of 'quo' used as an algebraic variable. "Quo modo?", "Quoque?", "Cui bono?", 'Quisnam?"... Starting from a very small fund of question words does not seem to have gotten in the way.
Language develops organically, that is: it expands and grows with the need for it. So for instance we wouldn't have the word "knife" prior to having the need to name the object. While there is a sense in which language can limit thought (see Sapir–Whorf above), language formation follows the need for its creation. Thus we had the concept of "time" before the word, when. We were showing each other how to do things before we even had language. We were presenting things, with two hands, for another to choose which, without ever speaking a word.
As Conifold hinted, language enables further conceptualization, but the leading edge of Thought is prior to language.
At first, look at similar question:
Could the existence of legs limit us in other ways of moving?
Well, there are other ways to move, but aside from any kind of transport legs seem to be the most efficient ones.
Same can be said of your question. There might be other ways to think, but either they are less efficient or they are not discovered yet. However, humans use written language for a few thousand years at least and spoken language is really old. Probably, if there were other kinds of using language to ask questions, they already would be discovered.
But still, it is possible that other ways exist. So, can it limit us? Well, these questions are better than nothing. But they can prevent people in discovering other forms of language. Yet, in overall, they enhance our capabilities, just like legs.
