1)
Why were these chosen to anoint Shlomo?
1.
Ralbag: It is proper that a king be chosen via the Kohen Gadol, Navi and Rosh Sanhedrin.
2)
What are "veha'Kreisi veha'Pleisi"?
1.
Refer to Shmuel II, 8:18:1:1-5 and the notes there.
3)
Why does it say "Al Gichon"?
1.
Radak: This is like "El Gichon." Also "va'Tispalel Al Hashem" (Shmuel I, 1:10) is like El Hashem, and "ha'Ramasah Al Beiso" is like El Beiso" (Shmuel I, 2:11).