Why did he first anoint Ish Boshes over Gil'ad?
Malbim: Anshei Yavesh Gil'ad loved Sha'ul.
Why does it say that he made him king "El Gil'ad"?
Radak: This is like Al, just "El he'Harim Lo Achal" (Yechezkel 18:6) [is like Al he'Harim], and other verses.
What are "Ashuri" and "Yizre'el"?
Radak: Ashuri is Beis Asher, like the Targum. Yizre'el is not the one in Yehudah, rather, in Menasheh's portion. 1
This is the correct text of Radak. (PF)
Why does it mention Ashuri, Yizre'el, Efrayim and Binyamin?
Radak: These places were on the way back from Machanayim to [Ish Boshes'] house in Binyamin. This was after the battle of the youths (of Avner and Yo'av).