As for unseen events:
WWIII to Enterprise
I pitched that to Pocket, but got no interest. It wouldn't feature enough familiar characters or elements to be marketable.
Portions of this were depicted in Jeri Taylor's Mosaic
. It didn't seem to be a single major war so much as a series of on-and-off border conflicts.
Invention of Transporters
Versions of this have been shown in the Wildstorm graphic novel Forgiveness
and the Lives of Dax
story "Dead Man's Hand," though neither is compatible with canon anymore. There was also an issue of Marvel's post-TMP comic that dealt with it indirectly.
The problem with exploring the invention of the transporter in the current continuity is that it would require revisiting ideas from "Daedalus," which was probably the worst 4th-season ENT episode other than the series finale and that has major continuity errors in it. (How could Emory Erickson have done research in an empty void of space a hundred light years in radius over a decade before NX-01 was launched, given that NX-01's crew were the first humans to go more than a hundred light years from Earth?)
We've seen a few of their adventures. The E-B in The Captain's Daughter
, "Shakedown" in Enterprise Logs, Serpents Among the Ruins
, and "Iron and Sacrifice" in Tales from the Captain's Table
, and the E-C in Well of Souls, Vulcan's Heart
, and "Hour of Fire" in Enterprise Logs