The weird thing about Section 31 is, if all the novels are to be taken as part of one's personal canon, that means that for a secret organization, they've been pret-ty damn loud. The Enterprise Incident and TUC come to mind.
Not really. Cloak
by SD Perry is ambiguous on whether or not it was Section 31's idea for the Enterprise
to steal a cloaking device from the Romulans; the only thing that's firmly established is that they later took that cloaking device and used it to conduct secretive experiments into the Omega Particle.
Nothing has been established in the novels linking Star Trek VI: The Undiscovered Country
and Section 31 other than that Admiral Cartwright was probably a member of Section 31. But that doesn't mean that they were in on the Khitomer Conspiracy. Doesn't mean they weren't, either; we simply have no data on it other than that Cartwright was involved with Section 31 in the 2260s.
My only complaint about Section 31 is that a lot of negative things that the Federation or Starfleet has EVER done on screen is now retroactively accredited to the group, which suggests a very haphazard leadership.
Again, not really. The only thing that the novels have specifically cited as being Section 31 retroactively is the Bak'u incident from Star Trek: Insurrection
and the "death" of Trip Tucker from "These Are the Voyages...."