1)
What is "Lehavros"?
1.
Rashi: It is an expression of a meal (the first meal a mourner eats after the burial).
2.
Radak: It is to feed even a small amount. Also below (13:6), it says "v'Evrah mi'Yadah."
2)
Why is it written Lehachros, and we pronounce it Lehavros?
1.
Radak citing Sanhedrin 20a: At first, they wanted to depose David/ When they realized that he had not told Yo'av to kill Avner], they came Lehavros (to give to him the first meal after the burial). Radak - some say so, but in all our texts it is written Lehavros.
3)
Why did David refuse to eat?
1.
Malbim: We fast over the death of Gedolim. David considered Avner to be great in Torah.