Reg Question 1
I would put the Hebrew name (As on the Ketuba)
Particularly with your example “Sarah Rivkah vs Sorel Rivil” where it isnt really a “yiddish name” but rather a dimunitive name. much like Somone known all her life as “Leahleh” would likely have “Leah” on the tombstone. Leahleh much like Sorel, Rivil arent realy Yiddish names
If it is a translation eg Tziporah and she was known as Faige/faigy all her life. Then I would probably write both “Tziporah Faygel”