Why does it say "l'Veis David", and not 'l'Achaz'?
Rashi: Because he was a Rasha, his name is not mentioned.
Radak: If not for David's merit, kingship would have ceased already from his seed due to their sins, and due to this king, who was a Rasha.
What is the meaning of "Nachah Aram Al Efrayim"?
Rashi: Melech Aram joined with Melech Yisrael to come against you. "Nachah" is feminine, for it refers to the Malchus (kingship). This is like "va'Yanach b'Chol Gevul Mitzrayim" (Shemos 10:14; it rested on).
Radak: "Al" is [with,] like "va'Yavo ha'Anashim Al ha'Nashim"(Shemos 35:22). "Nachah" - they came close to Yerushalayim, and pitched their tents there to besiege it and fight it. "Nachah" (feminine) refers to the Machaneh (camp) or Edah (congregation) of Aram, like "va'Tehi Aram", "va'Tehi Yisrael" (Shmuel II, 8:6, 24:9).
What is the meaning of "va'Yana Libo"?
Radak: He was very afraid.
Why was Achaz afraid?
Rashi: Each of these kings by himself already defeated Achaz - "va'Yitnehu Hashem b'Yad Melech Aram", "va'Yaharog Pekach ben Remalyahu Me'ah v'Esrim Elef" (Divrei ha'Yamim II, 28:5-6).
What is "k'No'a Atzei Ya'ar"?
Rashi: Barren trees make more noise than fruit trees (Bereishis Rabah 16:3). Malbim - the fruits make them heavier, so the wind moves them less. So they, who were barren of all merits and hope for Hashem's salvation, shook due to fear of the enemy.
Radak: They all move due to the wind, and one tree touches its colleague and makes it move. It is more than the motion of a lone tree. So everyone feared, and one makes others fear.