1)
What is the meaning of "va'Yar'em k'Som Levavo"?
1.
Radak: Just like there was straightness and purity in David's heart, so he tended them with straightness of heart and his Chachmah.
2.
Malbim: This refers to Torah leadership.
2)
Why does it say "uvi'Svunos Kapav Yanchem"?
1.
Radak: Tevunah (understanding) is attributed to the hands, for a shepherd conducts the flock with his staff in his hands, and he needs to conduct them with understanding. Even though understanding is in the heart, it is attributed to the hands, for they do the work. We find similarly "Sikel Es Yadav" (Bereishis 48:14).
2.
Malbim: This refers to running the country.