Noahides forbidden to study Talmud, Kabbalah
If a non-Jew observes the seven commandments, is righteous among the peoples of the world, and studies the seven commandments, then he is dear to the Most High, like a high priest who serves in the Temple.
From this it follows that a Noahide is obliged to study in detail everything related to the seven commandments and to know it perfectly. But he is forbidden to deal with other parts of the Torah.
Noahide can also study things that he is obligated to observe based on reason (such as charity or respect for parents) and even those things that he is not obligated to but has the right to perform (such as burnt offerings) .
2) The term "doing the Torah" refers to the study of the Torah for its own sake - a deep study and understanding of the commandments and their inner meaning. If the study is for some other purpose, it is not prohibited.
Seven commandments a Noahide is obliged to study at a deep level, and the rest - only for the sake of familiarization with them (not the way Jews study the Talmud). Therefore, a Noahide can study books where the laws are described succinctly (like the book of Rambam). If a Noahide does not understand something, he must ask a learned Jew for clarification.
3) Noahide can read the TANACH, including with comments. But he is forbidden to engage in the Oral Torah, which explains passages from the TANAH in depth. It is clear that a Noahide can recite sections of the TANAH as a prayer (such as the Psalms).
4) If a Noahide has a question for which there is no clear answer in the books, he does not have the right to solve this question on his own, but must turn to a learned Jew for clarification.
5) Noahide is forbidden to study Kabbalah, a secret teaching.
6) The study of the seven laws is not a separate commandment, because a Noahide does not have the obligation to study the Torah, and this is included in the seven commandments. Therefore, in this study, he has the merit of fulfilling the seven commandments, and not the commandment of studying the Torah. Nevertheless, since this study is related to his commandments, it is called "Torah studies" and the reward for it is very great.
If a non-Jew observes the seven commandments, is righteous among the peoples of the world, and studies the seven commandments, then he is dear to the Most High, like a high priest who serves in the Temple. About Shem, the son of Noah, who was a great righteous person, it is said ("Bereishit" 14:18): "And he is a servant of the Most High God."