What did Avshalom take?
Radak: He took this counsel for himself, to recall his name. The same applies to (Bamidbar 16:1) "va'Yikach Korach" (Sanhedrin 109b). He was remembered here afterwards; they took his bones from the big cavity and buried him by the Matzevah. That was his intent (to be buried there).
Why is "b'Chayav" written with only one Yud?
Radak: He lost Yud (10) years of his life for having Bi'ah with his father's 10 Pilagshim.
Why did he say "I do not have a son"? "Three sons and a daughter were born to Avshalom"!
Rashi: I do not have a son who can fill my place, who is esteemed like myself (i.e. fit to be king - R. Yitzchak bar Avdimi, Sotah 11a).
Radak (like Rav Chisda, Sotah 11a): We have a tradition, anyone who burns another's grain does not leave a son 1 to inherit himself. Avshalom had commanded his servants to burn Yoav's grain; his sons died in his lifetime.
Maharal (11a): Just like he burned what came from another's Zera, so his Zera (seed) is 'burned' (also his daughter died. If so, we must say that the father of Ma'achah (Divrei ha'Yamim II, 11:20) was a different Avshalom, like Malbim there, unlike Ralbag. - PF)
How would the Matzevah recall his name?
Rashi: It was an esteemed building.
Why was it called "Yad Avshalom"?
Malbim: He intended to buried there, but this was not fulfilled. He was buried in the forest 1 !
'Rashi' (Divrei ha'Yamim I, 18:3, citing R. Yitzchak bar Shmuel): He drew the form of his hand on the Matzevah.
