What is the meaning of "Chodesh Machar"?
Rashi: The moon is new. No one who eats at the king's table is absent on the 'Yom Tov.' Radak - everyone eats together on Rosh Chodesh like on Yom Tov.
What is the meaning of "Yashov Eshev"?
Rashi: I am always accustomed to sit near him.
Malbim: I want to sit with him also now. If not, I am like a rebel, for going away without permission! Therefore, v'Shilachtani - give to me permission to go.
What is "ha'Erev ha'Shelishis"?
Targum Yonasan, Radak, Malbim: It is the evening after the third day (from today). Radak - Shelishis is feminine, for it refers to Es (the time).
Why did David say that he will wait until the third night?
Rashi: If Sha'ul is not astonished at my absence on the first day, he will be astonished [and ask] on the second day.