Regarding the teaching of Torah to non-Jews, here are some of the Lubavitcher Rebbe's guidelines - reprinted from Chabad Talk
Encouraging Gentiles to Study Torah for Its Own Sake
In the Messianic era: “The sole occupation of the entire world”—Gentiles as well—“will only be to know G–d ... ‘As the waters cover the sea.’” This means that the “knowledge of G–d”—knowledge and comprehension—will envelop and conceal the existence of Gentiles until it becomes their entire being. Thus, [in order to prepare for this state of existence] some parallel to this must exist even now, by the Torah—in a comprehensible form—being found amongst Gentiles as well.
The Talmud states:
From where do we know that even a Gentile who occupies himself with Torah [related to the Noahide Code] is comparable to the High Priest? It is written, “That the man should keep them and live by them.” It does not speak of Priests, Levites, or Israelites, but of “the man.” You have thus learned that even a Gentile who occupies himself in Torah study is like a High Priest. The dictum that “A Gentile who occupies himself in Torah study deserves [divinely-imposed] death, as it is written, ‘The Torah that Moses commanded us is an inheritance’—an inheritance for us, and not for them” does not contradict this. For, “In that case [where Gentiles are encouraged to study Torah], it is referring to their seven [wide-ranging categories of] Mitzvot.” [Rashi explains that] “They occupy themselves with the laws of those seven Mitzvot to become expert in them.”
Gentiles should not only study Torah related to the Noahide Code for the purpose of knowing how to act, i.e., as a preparation and means for observing their Mitzvot. Rather, they are obligated to study Torah for its own sake. (The reason that this was not counted among their Mitzvot is that “positive Mitzvot were not counted [among the seven general Noahide laws],” just as the Mitzvah to give charity was not counted. )
It emerges that when Jews influence Gentiles to study Torah (in “their seven Mitzvot”), this is a fitting preparation for the fulfillment of the prophecy: “The sole occupation of the entire world”—Gentiles as well—“will only be to know G–d,” for several reasons:
When Jews influence Gentiles “to undertake the Mitzvot in which Noah’s descendants were commanded,” this refines the limbs of the body with which they perform these seven Mitzvot.
When Jews influence Gentiles to study the legal aspects of the Noahide Code to enable them to perform their Mitzvot, this refines the aspect of the mind that is related to the limbs of the body with which these Mitzvot are performed.
When Jews influence Gentiles to study Torah (in the laws of “their seven Mitzvot”) for the purpose of Torah study alone (not in order to know how to act, but in order to thoroughly understand the area of Torah relevant to them for its own sake), this refines the non-Jew’s faculty of intellect, by permeating it with comprehension of Torah. This is a fitting preparation for the era when “The sole occupation of the entire world will only be to know G–d”—knowledge of G–d for its own sake, and for no other purpose.
Furthermore, even the concept of “Keter [the Crown of] Torah” applies to Gentiles. This means that Torah [related to the Noahide Code] encompasses the non-Jew’s entire being. This resembles the prophecy that “[The earth will be filled with the knowledge of G–d] as the waters cover the sea.”
In the Sifri it is written: “The Crown of Torah is laid out so that the world’s inhabitants will not have reason to present a challenge [to G–d] ... the Crown of Torah is laid out for all the world’s inhabitants.” The simple meaning of the expression “inhabitants of the world” is a reference to Gentiles. In this case it is saying that Gentiles might come forward with a claim that they are entitled to receive the “Crown of Torah” in connection “their Mitzvot.” To this the response is given that “it is laid out for all the world’s inhabitants,” i.e., they can indeed attain the level of the “Crown of Torah” as well.
Based upon the above, even the prophecy that “The earth”—referring to all Gentiles—“will be filled with the knowledge of G–d as the waters cover the sea” has a parallel in the efforts of the Jewish people during the era of exile. We accomplish this by influencing Gentiles to study Torah related to the Noahide Code in a manner of the “Crown of Torah,” such that this study encompasses and permeates their entire being. This is similar to the prophecy: “The sole occupation of the entire world will only be to know G–d ... ‘As the waters cover the sea.’”
Hitva’aduyot 5745, Vol. 3, pp. 1838-1839.
Independent Value of Gentiles’ Torah Study
Gentiles should study Torah related to their Mitzvot, for they must study the details of their Mitzvot in order to be able to put them into practice. It may be said that their obligation to study the Noahide Code is not merely a “preparation for a Mitzvah,” but an obligation in its own right.
The reason for this is that along with the duty to adhere to the Noahide Code, they are obligated to keep these Mitzvot in a regular, natural manner, which necessitates previous study of the specific laws related to these Mitzvot. Thus, this study is not merely a “preparation for a Mitzvah,” but one of the Mitzvot in their own right, for otherwise [the Noahide Code] cannot be observed. Thus, this study has the halachic status of Torah study.
Hitva’aduyot 5749, Vol. 2, p. 447. cf. Likutei Sichot, Vol. 14, pp. 38-39