Stiles never mentioned the museum. As I recall he said, "You'll know them when you see them, they're painted like a giant Bird of Prey."
To which Kirk responded, "I didn't realize history was your area of expertise."
Stiles shoots back, "Family history, sir. There was a Stiles in the Star Service then."
As to why the Romulans went to war, and stopped the war, I can't say. My best guess is that when Earth started regaining their lost territories, The Romulans realized just how quickly it could get out of hand, especially if say the Vulcans, Andorians, Tellarites, et. al, were starting to get involved on Earth's side, and decided to cut their losses.