Likutei Sichos on Tefilla.
The Siddur.
Likutei Sichos vol. 39 p. 43 ff.

Chana’s Prayer, why and what we learn how to daven from Chana.

Rosh Hashana and Chana’s prayer.
Likutei Sichos vol. 19 p. 291 ff.

Likutei Sichos vol. 29 p. 182 ff.

Likutei Sichos vol. 22 p. 114 ff.
What Sefiras HaOmer teaches us about Davening and the Siddur.

Likutei Sichos vol. 35 page 125 ff.
The two types of day (morning to morning vs. night to night.

Likutei Sichos vol. 35 page 192 ff.
Silence in prayer: the Zohar and the Nigla- three levels.