1)
Why did specifically Yo'av and Avishai pursue Avner?
1.
Malbim: They were Go'alei ha'Dam (the closest relatives of the one murdered; they have a Mitzvah or Heter to kill the murderer).
2)
Why is it called "Giv'as Amah"?
1.
Radak: This is for a reason known to them. Perhaps an Amah (stream) was next to the hill.