Since to my best knowledge Mohammed was not literate - who, according
to modern research, actually   w r o t e  or take down notes from the
Prophet?

The answer appears to be complex, since the University of Pennsylvania
just held a conference on the subject:

"Who Wrote (Down) the Qur'an?"
Penn Humanities Forum
http://humanities.sas.upenn.edu/02-03/quran.htm

"Muhammad was illiterate his whole life and could neither read nor
write. His companions who knew how to read and write, transcribed the
Qur’an onto parchment and stone tablets to preserve it in writing as
well as by memory."

http://www.faithresource.com/showcase/Islam/islamoverview.htm

"The divine revelations continued to arrive in bits and pieces over a
period of  twenty-two years until his last days in 632 C.E. Whenever
these revelations were received the prophet would memorize them. At
the first available opportunity he would recite them before his chosen
companions. These intimate helpers and friends of his would write the
dictated message on the pieces of parchment, skins of animals, dried
animal bones, wooden tablets, soft stones, leaves of palm trees and so
forth. Many of his dedicated companions memorized as many of the
revealed verses as they could. From time to time these companions used
to review the revealed verses with their prophet. One of the better
known young scribe and the secretary to Muhammad in taking dictations
was Zayd ibn Thabit. He also used to arrange the bits and pieces of
the revealed verses under the direct supervision of the prophet."

http://www.mostmerciful.com/chapter-1.htm

Here you'll find the names of the Prophet's companions, and
information about each of them:

http://islamicweb.com/history/sahaba/

Try this site:

http://www.abdulmalik.net/islam1.php