The Crystal Warriors by William R. Forstchen and Greg Morrison
From review on goodreads.com:
A group of American soldiers are being chased by some Japanese
soldiers somewhere in China during World War Two. They stumble across
an ancient temple, and both the Americans and the Japanese are pulled
through to another world.
This sounds to me like the Dragonlance legends trilogy, specifically the last book of that trilogy Test of the Twins.
The man recording everything that happens would be Astinus of Palanthas, during the final book of the trilogy (iirc) Test of the Twins, the primary character Raistlin, is found or bought to the great library of Palanthas recorded by Astinus, ...
Well, if this comment by "alexwlchan" is correct:
JKR touched on money in an interview. “There is legislation about what you can conjure and what you can’t. Something that you conjure out of thin air will not last. This is a rule I set down for myself early on.” [...] Sixth question down: http://www.accio-quote.org/articles/2000/0700-swns-alfie.htm
The book A Touch of Magic by Gregory L. Mahan has many similarities to what you describe:
Magic is outlawed except by those under control of the king/elite
Main character found a book of magic
Main character meets/learns from imp
Main character in exile
Differences from what you describe include:
Recent - published in 2011
I don't recall ...
Perhaps Mercedes Lackey's The Outstretched Shadow? It was published in 2003, which is a little out of range but close. From memory, and it's been a while since I've read the series myself:
The main character is the son of a (or The?) high mage, but struggles with the formal magic system.
He finds a book to teach him Wild Magic in the city market
He learns ...