Sounds about right! We can perhaps also add that he was reasonably aware of the basic tenets of Judaism and Christianity (based on the Constitution of Medina), and that he was quite charismatic. He being a merchant beforehand also sounds quite reasonable, as we have a Christian source (the Armenian Pseudo-Sebeos) from the 660s referencing that. But yes, anything more than that is debatable. I don't think we can even nail down his year of birth or death, since the traditional Year of the Elephant doesn't quite work for his birth (the last inscription of Abraha, the man who allegedly invaded Mecca with an elephant, was from 553), whilst Stephen Shoemaker's Death of a Prophet (2011) raised some very interesting question about what the early sources say about Muhammad's death - was it in Medina as the traditional narrative has it, or was it whilst the Prophet was leading an invasion of Palestine? I quoted a lot of the sources cited by Shoemaker here, and various other sources mentioning Muhammad in the seventh century here, so you can take a look at the evidence for yourself :)

Uttered the Quran

I believe the Qur'an was put into writing decades after his death. Realistically, how likely is it that Muhammad is the single author of the Qur'an?

If we are talking about near certainty, I think the list is much narrower.

1. He spoke some variety of Arabic.
2. He lived in the early part of the 7th century, but did not live to 650 AD or beyond.
3. He led 'Arabs' in battle in the region around the Northern Arabian peninsula (Arabs being not itself a clear category).
4. He claimed prophetic status, which is reflected in the title "Muhammad."
5. He was very concerned with the Last Judgment.

We probably do not, on the other hand, know with certainty what his personal name was (MHMD surely being a title), where he was born, when he was born, where he lived, what his relation with the Qur'an was, which Arabs he ruled, and what his theology was. Muslim tradition tells us enormous amounts of detail about all of these points, but it suffers from being extraordinarily late and tendentious. For example, the traditional Muslim chronology of Mohammad's life is extremely artificial and uses magical numerology.