Can women become a surgeon in accordance to Halacha or a judge in a court ?
ב"ה Shalom In regard to the study of medicine there is no reason in the study of medicine itself for a woman to refrain from studying medicine. Women may be doctors or surgeons just as they are nurses and medical technicians. They may also treat men if necessary, of course all in accordance to Halacha and modesty. In regard to the issue of being a judge, there are two aspects to the question. One is the very dealing with law which is not according to the Torah, which is forbidden even for a man. Therefore it is forbidden to be a judge. (See Rav Eliezer Waldenberg zt"l שו"ת ציץ אליעזר יב פב , Rav Avraham Shapira zt"l Techumin 3, pg. 239, Rav Ovadya Yosef zt"l, שו"ת יחוה דעת ד סה) All that has been said until has to do with dealing with secular law. Now the question arises can a woman be a judge for Jewish law. This the Shulchan Aruch (Choshen Mishpat 7:4) makes simple and clear that she may not be. This is because the Torah has a unique attitude to the issue of testimony and women and the Talmud (Nidda49b, Yerushalmi Shavuot 4:1) stipulates that one who may testify may also judge. However, women who may not testify may not be judges. The question then arises how do we explain Devora fromthe Tanach who was a judge? Different explanations have been offered. One of them that Devora was an exception and it was decided by G-d's word that she may be a judge.(Tasafot Nidda 49b) Others say that although she had the title of a judge she didn't actually function as a judge but she would teach the other judges.( פסקי הראש על שבועות ד׳:ב׳:) Others say she was more of a consultant but not actually a judge.( חידושי רמב"ן על שבועות ל׳ א) There is a lot more to be said on this issue, however I have only brought major points. All the best