What is the meaning of "va'Shem Anahu"?
Radak, Targum Yonasan: Hashem said to him via a spirit of prophecy.
Malbim: Hashem answered him. Shmuel saw that the time was coming, and knew that the chosen man would come. He was pondering if this is him.
What is the meaning of "Ya'atzor b'Ami"?
Rashi: He will rule over them. This is like "Atzur v'Azuv" (Devarim 32:36). A ruler must restrain the nation in war, Lot] they scatter and separate from each other, and to stop everyone from doing evil.
Radak: He will be king over them. This is like "Yoresh Etzer" (Shoftim 18:7). A king is called "Otzer", because he stops the nation from going or acting without his permission.
Radak citing Targum Yonasan: He will remove the subjugation from My people. I.e. he will stop the Pelishtim and prevent them from making war with Yisrael.
Malbim: He will stop them from their evil path, and through this he will merit to save and be saved.