1)
Why did he say "v'Chazakta v'Hayisa l'Ish"?
1.
Radak: Be zealous and rule over yourself, and suppress your Yetzer. Also Yonason translates 'be a man who fears sin.' Also "v'Amasa Ben Ish" (Shmuel II, 17:25) means [the son of] a great, honored man, and "Kulam Anashim" (Bamidbar 13:3) means great and honored.
2.
Malbim: Chazal say that Shlomo was 12 at the time. In Divrei ha'Yamim I, 29:1 it says that he was "Na'ar v'Rach." In David's lifetime, he stood by him both in conducting the nation and teaching to him Torah and Musar. Now that David is about to die, Shlomo must strengthen himself in conducting the nation, and not fear any person, as is proper for a ruler.
