Why did he say that he wishes he were Shofet in the land?
Malbim: He shows that he does not desire the crown and kingship, only to be a judge, to remove stumbling in sin.
Why does it say "v'Alai Yavo"?
Radak: This is like v'Elai. Many verses say Al in place of El.
Malbim: I will judge them alone, without an intermediary. 1
Even if the man is not Elai (from my family or Shevet), I will vindicate him (as opposed to David, who cares only about his own Shevet. It seems that this is Malbim's intent.)
'Alone' implies without other judges. 'Without an intermediary' implies that people can go directly go him, and need not ask others to request that Avshalom hear their case. (PF)
What is the meaning of "v'Hitzdaktiv"?
Rashi citing Targum Yonasan: I will judge him truthfully.
Malbim: I will vindicate him. (Riv refers to a quarrel; Mishpat means that the verdict is like he says, like it says about Benos Tzlafchad "Mishpatan" (Bamidbar 27:5).)