Some murder weapon speculation:
Some type of dart perhaps. A south-American hitman that uses curare blowgun darts as his tools of the trade? Or more seriously some exotic poison tipped rope-darts, those would explain why there are no physical evidence left behind without the need of a huge conspiracy involving the daughter/guards/officials
treave was the man in black in Du Yao's study masked?
Does Cao'er have knowledge of darts/blowgun darts/rope-darts?
A1xA
We're asking in the first choice and not demanding. No need to try and make her propose it.
I can't decide for the second option, killing a child is probably the worst choice.