FWIW, I think the most likely source for the ballet is Bolshoi in Moscow - it's big, it's famous, and we know they're in the area. The main stage is closed for renovations right now but performances are continuing on the "New Stage." I've tried to track down conclusive pics but nothing yet... y'all are better Googlers and might have more luck.
The costumes are traditional Russian and could be anything from Bolshoi's extensive wardrobe. Bolshoi is closed on Mondays and my guess is November 21 was the date of filming there before leaving for the land down under. I was hoping to get some conclusive weather reports from that day in Moscow, but it was pretty much cloudy the whole month of November. Anyway, this timing leaves time for an unknown SA/Europe leg at the beginning of the race. Guessing SA for now.
EP1: Denver (Red Rocks Amphitheatre) (11/7) to Sao Paulo, Brazil (bridge, airstrips, yellow helicopter)
EP2: Sao Paulo to S.A. DESTINATION 2
EP3: S.A. to Segesta, (Sicily) Italy (ruins)
EP4: Segesta to Corinth, Greece (diving into canal)
EP5: Corinth to Moscow, Russia (11/21??) (St. Basil’s, ballet)
EP6: Moscow to Perth/Rottnest, Australia (11/24) (newspaper)
EP7a: Perth/Rottnest to Darwin (11/25) (newspaper/sighting) TBC
EP7b: Darwin to Adelaide (11/26) to Lopburi, Thailand (masks, monkeys, Buddha)
EP8: Thailand leg 2? Lopburi/Attathaya? (11/27-28??)
EP9: Lopburi to Tokyo (11/29-30??) (shopping district, Mt. Fuji)
EP10: Tokyo to Anchorage (12/1) (sighting, red plane)
EP11: Anchorage (12/2) to Denver (12/3)
I think someplace has a 2nd leg that we don't know about -- for now, I'll guess Thailand since we have a couple different locations confirmed there.