Dr Marijn Van Putten (2019) recently authored an insightful paper on the subject of the codification of the Qur'an under the supervision of Caliph Uthman during the middle of the 7th century (roughly two decades after the death of the Prophet Muhammad), based upon the examination of 14 early Qur'anic manuscripts. The vast majority of known Quranic manuscripts (all but the Sanaa palimpsest, in fact) are of the Uthmanic text type, and only minor variations are present in this text type.

He concludes that there certainly was a single written archetype from which all Quranic manuscripts of the Uthmanic text type are descended. Whilst it is impossible to prove that the standardization of the Qur'an did not take place before ʿUthmān’s reign on the basis of this data, the manuscript data we do have access to is consistent with the traditional account regarding the its standardisation during the mid 7th century based upon a single archetype.

Regarding the views amongst other secular historians as to its compilation; Wansbrough^(1) (1977) famously argued that the Quran was not compiled until two or three hundred years after the Prophet’s death, whereas Burton^(2) (1977) argued that it had been compiled by the Prophet himself rather than by ʿUthmān. Since then many authors have weighed in on these questions, but no clear consensus has emerged.

Regarding the second part of your question, which alludes to authorship of the Qur'anic archetype itself rather than mere standardisation of the text, there is unfortunately no clear consensus here either amongst secular historians. Muslim historians on the other hand (obviously) unanimously attest that this text was authored by God Himself, as the Qur'an itself consistently affirms. However to investigate such a claim would go beyond the realm of historical enquiry, so it's not something that you're going to acquire a conclusive answer for here. That said, whilst the Prophet Muhammad being illiterate is not something that can be decisively vouched for, it isn't a surprising claim given the fact that the overwhelming majority of medieval and ancient societies, irrespective of their profession tended to also be mostly illiterate. From my limited knowledge of this, exceptions to this would have been the clergy, scribes, civil servants and educated nobility.

[1] Wansbrough, John. 1977. Quranic Studies: Sources and Methods of Scriptural Interpretation. Amherst, NY: Prometheus Books.

[2] Burton, John. 1977. The Collection of the Qurʾān. Cambridge: Cambridge University Press.

I would expect there isn't much certainty on how the quran was written, but do historians have speculations on how it could've been written?

There is considerable consensus among secular historians, that the text which is today known as the Quran was compiled in Iraq several decades after the death of Muhammad under the auspices of the first caliphs. The source material from which the Quran was compiled would have been a more diverse grouping of (inter)related texts which would have been compiled during and after Muhammad lifetime, or ascribed to him; in which case texts might have formed part of or been inspired by an earlier Christian, Jewish or Persian traditions.

This would have been done by a group of people familiar with religious scripture and/or intimate knowledge of Muhammad's teachings under the authority of a caliph. Islamic tradition attributes this process to Abu Bakr, who allegedly ordered Zayd ibn Thabit (Muhammad's personal scribe) to compile a single manuscript, which was later standardized under Uthman. This however, while not implausible, would still have to represent an idealized version of actual events as the earliest (partial) manuscripts of the Quran known to science today show differences with the later 'common' version.

Compared to the Christian gospels however, the process of standardization was relatively quick, owing to the fact that following Muhammad's death his direct companions formed the elite of an empire, rather than individual and scattered proselytizers.

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How plausible is it that a succesfull merchant in arabia such as muhammed was illiterate? is there reason to doubt his illiteracy?

In mainstream Islamic tradition, the illiteracy of Muhammad is first an foremost used as a rhetorical device to prove the Qurans veracity, as it is held that an illiterate man could have never compiled the form and contents of the Quran. However, there are also Islamic traditions which state that Muhammad learned to read and write after receiving his revelations and there are scholars who do not think Muhammad was illiterate at all.

His purported illiteracy is not implausible. Long(er) distance trading predates the invention of writing itself and in a more practical sense, having a scribe would have circumvented the need for an individual merchant to be literate while still incurring the obvious benefits of literacy and the use of scribes by Muhammad is documented. In any case, the question of Muhammad's literacy isn't that relevant, as history has many examples of both literate as well as illiterate poets (Homer for example) producing high quality prose and poetry.

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I've heard that the quran is a very impressive text in terms of its prose in the original arabic. Would it take a skilled writer to have written the quran? how hard were those to come by in arabia? I've heard that there was a literary/poetic tradition in arabia, presumably that would provide for a decent supply to skilled writers to have written the quran?

The Quran is certainly a much more compact text when compared to its Christian and Jewish counterparts. It consists (depending on the language) of about 75000 words, whereas the New Testament has about 180000 words and the Old Testament/Torah has over 600000 words. In terms of its form the Quran is certainly more aesthetic, being poetry as opposed to the narrative style of the New Testament and the Torah.

Would it have required considerable talent to compose it? Yes, it would have. At the same time, as stated before, scholars place the codification of the Quran as happening in Baghdad/ Iraq. This was not a provincial backwater but the capital of an empire situated on major trade routes in a region possessing the worlds oldest recorded civilizations. It would have had many literate people, many of them intimately familiar with Jewish or Christian scripture and themes as these religions were dominant there at the onset of Islam.