Glory to Rome!
"Let each man pass his days in that wherein his skill is greatest" Propertius Sextus
Found the answer to #2 while browsing the official Catan site: http://catan.com/faq/29-catan-cardgame-cards/1366-traveling-...
Traveling Theater - Can I move the Traveling Theater without trading a resource for a star?
No; you must trade when you move the Traveling Theater.
I guess it sort of implies that you have to move it to trade a resource for a star. Any other opinions?