LF: There is a Chiyuv on the Beis Din to try to avoid getting to the point where you actually have all of the requirements for execution.
rob: Kippah can (in theory) be for anything, according to the Gemara, though some Rishonim try and limit it.
Health: The truth is that in 1678 Yemenite Jews remembered the cordial relations they had with their neighbors and rulers for the previous century or so. And then a ruler who didn’t like them got up and most of them were killed. That’s what our relationship under Muslim rule was like for a millennium. Cordial and happy, until they decide to kill us.