Secondly (and I've brought this one up in the past as well)
The Han mangonel (catapult):
A disclaimer straight away: I do not speak Chinese, so I can't confirm terms first hand or use primary sources.
The current name is a literal translation of the word "trebuchet" into Chinese. (Traction) catapults in Ancient China instead actually were referred to as
"砲pào", the same word that is later also used for cannons. In the much later Song dynasty catapults were also classified by the number of wooden spars making up the catapult's arm. The 3D model in-game has one only which would make it a "single-beam trebuchet", a "筲砲砲Dān Shāo Pào", though the frame looks a bit different. The same military compendium also mentions the "crouching tiger" catapult, the "虎蹲砲Hǔ dūn pào" which looks pretty similar to ours. However, in my opinion this last name is way too specific, and seems exclusive for the Song period.
Therefore, I suggest the following change:
Tóushí Chē -> Pào or Dān Shāo Pào (and just maybe Hǔ dūn pào)
Sources: