In the same way that we also call the Ottoman Empire by the name of its ruling dynasty, it's perfectly normal to refer to different Chinese states, at least post-Mongol invasion, by the name of their ruling dynasty. Qing should absolutely be accepted as a type-in.
I definitely thought the "Georgia" question was referring to the country of Georgia (don't come at me, I'm not from the USA so I'm not familiar with small historical facts like that) and I took so long trying to think of a costal city that isn't overly obscure.
Maybe specify that the bouncy tree product was introduced to *European* science at that time? The Olmec, Aztec, and Maya were using it long before. (You might argue that what they were doing was engineering rather than science, but that would be an overly strict definition of science, IMO.)
I can't even get historical sports questions right. I had an image in my head of British people walking around on a lawn, but I couldn't remember the word "cricket." Twice now.
Also, I can thank my boxes of 64 and 128 for the cobalt answer.