The Rebbe's letters on free will, Divine Providence, miracles, and reward and punishment:
Free will. G-d knows everything, including our future choices, yet this does not negate human free will; the two coexist without contradiction (IK 439, 6741, 5883). Every Jew has true free will because his essence is rooted in G-d Himself (IK 7831). Choosing a life of Torah and mitzvos with one's free will brings special Divine help (IK 8523). On whether marriage matches are decreed or freely chosen, see IK 264.
Divine Providence. Divine Providence operates constantly, even within nature, and every event carries G-d's guidance (IK 10751). Each person's presence in a particular place and time is by Providence, for a purpose (IK 3294). On how the early authorities, Kabbalah and Chassidus understood Providence, and the Baal Shem Tov's teaching of individual Providence over everything, see IK 094, 405.
Miracles and natural means. Miracles beyond nature can occur for individuals even today (IK 2140), and recognizing miracles should inspire gratitude and further good (IK 4718, 7238). Trust in G-d is essential, but making natural efforts — a "vessel" — is usually required as well (IK 256), including following expert medical advice (IK 3110). Belief in miracles should be instilled honestly from childhood (IK 8492).
Reward and punishment. On reward for beautifying mitzvos, see IK 126; on whether punishment can be a natural consequence, see IK 8555; on Gehinom, see IK 9982. Supporting the publication of Torah and Chassidus brings lasting merit, spiritual and material (IK 193, 205, 276, 281).
See also: Faith and Chassidus – Faith and reason; Bitachon – Everything happens for a reason (Divine Providence); Bitachon – Trusting G-d and doing your part.