These two chapters do not offer a lot with regard to doctrines.
Some History and the First Battle
In chapter 9, we learn how Zeniff and his people came to the Land of Lehi-Nephi or the land where Nephi took his people to settle (away from Laman and Lemuel). The Nephites dwelled here for many years until Mosiah (the first) departed from the Land of Nephi and found Zarahemla (Omni 1:12).
Zeniff and those who followed him desired to re-posses the Land of Nephi. As they traveled in the wilderness, they "were smitten with famine and sore afflictions; for [they] were slow to remember the Lord [their] God" (Mosiah 9:3).
One they arrived, the king of the Lamanites granted them a place to live. They lived in peace until the Lamanites killed some Nephites in order to take their flocks and corn. This incident started the first battle between Zeniff's people and the Lamanites.
"In the strength of the Lord" the Nephites went to battle. They prayed and cried mightily to the Lord that He would deliver the Nephites out of the hands of the Lamanites. They remembered how the Lord had delivered their fathers and they trusted that the Lord could deliver them. And "God did hear [their] cries and did answer [their] prayers (Mosiah 9:18).
The Nephites lost 279 while 3,043 Lamanites will killed in the battle.
Peace and the Second Battle
For twenty-two years, Zeniff and his people lived in peace and prospered in the land. King Laman died and his son became the new Lamanite king. The new king begins to stir up the Lamanites to fight against the Nephites.
Zeniff then explains to his people why the Lamanites hate the Nephites. He reminds them of the choices Nephi and Laman and Lemuel made and the eventual consequences of their choices. Is it any clearer to see how Nephi, by obey the Lord, was blessed and how Laman and Lemuel were cursed for not keeping the commandments?
Zeniff prepares his people again for battle and they put their trust in the Lord (Mosiah 10:19). The Nephites slaughter the Lamanites … so many that they did not number them. Then after the battle, the Nephites did not begin a counterattack, but instead they returned to their lands and tended to their flocks and fields (Mosiah 10:21).
History of Abinadi
We do not know the history of Abinadi … the scriptures do not tell us where he came from or how he received his mandate from the Lord to preach repentance. But we can reasonably assume that Abinadi was born in Zarahemla and came with Zeniff and his party. If that is the case, then we know that Abinadi was "smitten with famine and sore afflictions" along with everyone else as they journeyed in the wilderness (Mosiah 9:3). We can probably assume the Abinadi fought the Lamanites in the two mentioned battles. We can reasonably assume that Abinadi saw that Zeniff tried to keep the Lord's commandments and was a good man.
Perhaps Zeniff's speech on the Lamanites' beliefs sunk deep in Abinadi's heart; particularly the part where Zeniff said, "Nephi was more faithful in keeping the commandments of the Lord - therefore he was favored of the Lord, for the Lord heard his prayers and answered them, and he took the lead of their journey in the wilderness (Mosiah 10:13). Perhaps Abinadi knew he was favored of the Lord and he "took the lead" in calling King Noah to repentance. All this is speculative, but it may not be a far stretch.
The one thing that is certain and undeniable is the impact this one man would have on the remaining history of the children of Lehi.