Joseph,
1. Google “Can a Jew serve as a secular judge?” I would add that where the Jews are non-observant there is no issur of ????? ???? ????? (see Iggerot Moshe YD 1:72).
2. If you are talking about a ????, there is no issue regarding gentiles. Regarding Israel, Rav Shaul Yisraeli says (Amud HaYemini 12:5 – available on-line) that it only refers to a position held for life and passed on to the incumbent’s son . Someone who can be turned out of office by the public or does not hold the position for life or whose son does not inherit it does not hold a ????. Rather (s)he is an employee of the public – and anyone can be an employee.
3. Rav Yaakov Ariel says that it is a mitzva for someone who can rule in such a way that the ruling will be upheld on appeal and is in line with the Halacha to be a judge. He also encouraged a certain knowledgeable woman to study Law and pursue a career in public service.