Who is "Beis ha'Melech"?
Radak: It is his wives. He did not leave any of his wives, only the Pilagshim to guard the house. He did not take a carriage for the women, for they left hastily - "Kumu v'Nivrechah
Why does is there a silent Lamed in "veha'Lechem"?
Radak: There is no reason for it. I wrote why such letters appear in Tanach (refer to 15:21:1:1). We find a superfluous prefix Lamed, e.g. "Hargu l'Avner (3:30), "veha'Shelishi l'Avshalom" (Divrei ha'Yamim I, 3:2).
Why did he not mention the raisins?
Radak: They are included in Kayitz. All dried fruits are Peros Kayitz.
Why did none of the Ashirim of Yerushalayim bring a horse and provisions to David, only Tziva?
Malbim (3): Those who fled, they rushed to flee. Those who remained feared to show that they love and support David. Only Tziva slandered his master, to make him fall in any case. He told David that he himself gives the gift, and he could tell Avshalom that his master sent the gift to David.