Under what conditions may one teach non Jews Torah? Does it matter if it is written or oral Torah? halacha , hashkafa etc..? What if one’s job depends on it [i.e. a professor, a "chaplain" who must speak to Jewsh and no Jewish inmates, patients all at once ? Thank you

You can teach a non-Jew the laws of the Torah specific to his observing the seven Noachide laws or those moral obligations that are universal to all mankind. It would seem reasonable that these should be the subjects addressed by a chaplain speaking to a mixed audience. You are also allowed- in defense of the Torah- to answer a non-Jew’s questions or criticisms regarding Judaism (Shu”t Yabiya Omer 2 Yoreh Deah 17). If you are teaching a Jew Torah it is unnecessary for you to break off if you see that a non-Jew is listening in.