The Rebbe's teaching on Pnimiyus HaTorah — the inner dimension of the Torah, Kabbalah and Chassidus:
A mitzvah of our generation. The purpose of existence is to serve the Creator, and in our generation there is a mitzvah to reveal Pnimiyus HaTorah (IK 5947). Its study is essential for rectifying the cause of the exile and bringing the redemption (IK 7721), and it is a necessity for everyone, including a young man preparing for a shidduch (IK 6167). The claim that there is no obligation to study it is mistaken: rulings in Pnimiyus HaTorah, like rulings in monetary and ritual law, require expertise in that field (IK 8729).
In daily life and in teaching. Seeing G-d's kindness in material matters is a hint to add in spiritual matters, including the study of the inner Torah (IK 3600). Sacred work calls for more inner strength and Torah study, especially Chassidus (IK 3602). Torah study, especially Chassidus, should be adapted to each student's qualities (IK 3719). Pesach night is a time of revealed G-dliness and of learning the inner Torah (IK 8616).
Specific questions. Matching in marriage and palmistry are discussed in Kabbalah and do not contradict the command to be wholehearted with G-d (IK 5383). On the Zohar's account of Adam's expulsion from Eden, see IK 8555.
See also: Kabbalah – Studying Kabbalah; Torah study – Learning Chassidus; Jewish outreach – Spreading Chassidus (hafatzas hamaayanos); Moshiach and Geulah.