How were his hands taught war?
Malbim (Tehilim 18:35): He learned war strategy. Even so, he did not fight.
What is the meaning of "v'Nichas Keshes"?
Rashi: It refers to drawing a bow 1 - "Chitzecha Nichasu Bi" (Tehilim 38:3).
Radak: The bow was broken in my hands. Malbim - there was no need to use it.
Rashi: I have the strength to draw it. David had [Nechushah] bows in his house. Nochri kings came and saw them, and said 'do you think that he can draw them?! They are merely to scare us! David heard, and took them and broke (Rashi Tehilim 18:35 - drew) them in front of them.
What is the root of "v'Nichasah"?
Rashi #1 (Tehilim 18:35): The root is Nichas. In the passive form, the second Nun is omitted, so it says Nichasah in place of Ninachtah. This is like Nichar Geroni (69:4) in place of Ninchar, or "Nachar Mapu'ach" (Yirmeyah 6:29), Nidaf in place of Nindaf, "Eini Nigra" (Eichah 3:49) is in place of Nenagra, Nitnah in place of Ninasnah. Just like Asah (in passive feminine form) becomes Ne'estah, and Anah becomes Ne'enasah.
Rashi #2 (Tehilim 18:35): The Nun is not from the root. Rather, it is like "Nechlu" (Yirmeyah 12:13, an expression of Choleh (illness)). It is as if it says v'Nidrechah Keshes (a bow was drawn).
Why does it say here "v'Nichas Keshes", and in Tehilim (18:35), "v'Nichasah Keshes"?
Radak: Keshes can be masculine or feminine.
What is "Nechushah"?
Rashi (Tehilim 18:35): It is copper.
Radak: It is hard like Nechushah (very strong iron). The same applies to "v'Es Artzechem ka'Nechushah" (Vayikra 26:19).